When taking a verbal as a direct object, certain verbs require a gerund participle and others an infinitive, in most cases marked:
He abhors going to the beach.
She wants to go to the beach.
The vast majority of verbs can take either:
I love swimming in the ocean.
I love to swim in the ocean.
A ThoughtCo article lists 56 common verbs requiring a gerund-participle and 59 an infinitive. The choice of one or the other is highly idiomatic with errors by native speakers quite rare. This would be a grammar point, then, only of interest to ESL learners.
What you are asking, however, is 1) whether the same preference is exhibited when the governing verb is in a relative clause in the subject and the verbal is a predicate complement and 2) whether that preference could be distilled into a general rule that neatly follows the ThoughtCo. list.
First off, if the construction is reversed, i.e., the gerund-participle is the subject and the relative part of the predicate complement, all bets are off:
Racing motorcycles and winning was all he ever wanted to do. — Amazon blurb for: L. M. Carr, From a Distance, 2017.
With the relative first, one would expect:
All he ever wanted to do is race motorcycles and win.
Since to do is already marked, to can be dropped from the infinitives race and win, even though they are in separate clauses.
The verb want seems most consistent in attracting an infinitive in the complement clause:
What she wants is to see merchandise, to learn about it, and to compare it. — Department Store Economist 13 (1950), 26.
In one sentence, what every woman wants is to make sure the man in whom she trusts will not turn into her main aggressor later. — “Women Tests,” Heptagrama.com.
The last thing that any consumer wants is to pay for a costly repair, only to have to battle corrective maintenance after the job is done when repairs are not completed by certified mechanics. — “Engine Rebuilding,” Long Beach Auto Repair.
Gerunds are less common, but do occur among native speakers, mostly in informal speech:
Every moment spent in his house makes me fall further and further in love with him. Talk about chiselled abs and hard muscles! I don't care about his billions. All I want is being with him forever. But he's damaged goods. — Mia Ford, Next Door Daddy, 2017.
My Mom isn’t that old. The last thing in the world I want is seeing her undergoing any surgery, especially something like knee surgery. — Wendy Polisi, “Essential Oils for Arthritis,” Blog post, 26 Oct. 2018.
The last thing anyone wants is realizing your home alarm system is malfunctioning, just as you are about to hit the road. — The Gremlin (Garden Route, Klein Karoo, South Africa), 1 Nov. 2018.
The last thing anyone wants is discovering their security systems is on the blink before leaving for vacation. — Delco Alarm Systems, 31 July 2019.
But in China, you can't charge a lot for music, so what TME really wants is selling more entertainment products to boost its income. — Forbes, 12 Dec. 2018.
The last thing anyone wants is buying a holder that is too small, too big, bulky, or unattractive. “Top 10 Best Makeup Brush Holders for 2019, TopReviewPro.
Although acceptability is not an objective criterion, some of these sentences sound less idiomatic than others, and I would likely have used infinitives in each case.
With other verbs, the choice seems less clear.
The verb abhor takes a gerund-participle as object. When it occurs in the construction you’re asking about, the preference is also for a gerund-participle:
What I abhor is the genuflecting of the national media who dutifully grovel at the soft-spike saddle shoes of the Augusta National membership. — “The Augusta Question,” Communication Links, 11 April 2012.
What I abhor is placing blame on something that is NOT the cause of the problem. — Supercell Forum Post, 4 June 2018.
Again, infinitives also occur:
What I abhor is to be referred to as a musician, or a composer, as if that’s it in some academic sense. — Kenneth Gaburu, interview, Nicholas Zurbrugg, ed., Art, Performance, Media: 31 Interviews, 2004.
I would not consider being referred to as more felicitous than the infinitive in this sentence, though others might.
Both verbs are listed as taking gerund-participles as objects, a preference also observed in the relative-gerund construction:
James is no gym rat. All he recommends is improving things gradually, going for walks, cutting back on drink and junk food. — London Real Academy, 26 April
Now, what we are recommending is using SiteGround. SiteGround is going to do something called managed WordPress hosting, which makes it really easy for you to get your site up and running. — “Setting Up WordPress,” Food Blogger Pro.
First and foremost, what we recommend is focusing on foods that are unpacked with just 1 natural ingredient — themselves! — “Decoding Ingredients Labels: Why it's Important to Read them and What to Look for,” Plant B, 6 May 2019.
What I would suggest is buying the other editions so that you can use the additional cards with the Duet rules/legend keys. — BoardGameGeek forum, 18 Nov. 2017.
I’m not advocating living without indulgence. All I’m suggesting is regulating it. And being aware of when we’re indulging... Gul Panag, “Physical Fitness Makes Me More Objective,” ThriveGlobal.in, 24 Oct. 2018.
Infinitives, however, occur far more frequently with recommend and suggest than gerunds with want, also in edited publications:
All he recommends is to grill them over wood or charcoal for better flavor, get a good char on them, and to immediately "kiss them with quality extra virgin olive oil" after they're off the heat. — “Hold the Burgers: Meatless July 4 Grilling Ideas,” NBC New York, 1 July 2016.
All we recommend is to take them along with water. — “Vitamins,” Super Brain Food Club.
Now on that subject, when we transplant into this particular technique, what we recommend is to remove the plastic outer wrapping and to do so without actually damaging the existing roots. — Jeffrey Winterborne, Medical Marijuana Cannabis Cultivation, 2008, 47.
The second thing I want to suggest is to move from comprehensive to what we like to call adaptive planning. — The Challenges of Providing Future Infrastructure in an Environment of Limited Resources, New Technologies, and Changing Social Paradigms, 1995, 25
Something I strongly suggest is to rotate your students’ seats. — Renee Rosenblum-Lowden, with Felicia Lowden Kimmel, You Have to Go to School … You’re the Teacher!, 2007.
What I am suggesting is to stop focussing on exercise solely as a means to weight loss. — The Skinny on Exercise, Weight Solutions for Physicians.
So what you're suggesting is to spend our time and resources investigating this and not focusing on outsourcing or any other types of big initiatives? — Daniel C. Melchior, Jr., Shared Services: A Manager's Journey, 2011.
What you're suggesting is to lock a mongoose in a cage with a cobra. You are the cobra and you are assuming that the cobra will win. — Mike Bird, Iskandar: And the Immortal King of Iona, 2013, 75.
I find none of these sentences objectionable; some usages of the infinitive actually seem preferable.
Whether certain verbs take an infinitive or gerund-participle object is an idiomatic feature of the language which could be distilled into a grammar point for ESL learners. Attempting to apply this feature to other grammatical/syntactical contexts is highly predictive for the verb want, but can only establish a preference of various strengths for other verbs. It is not necessary to plough through ThoughtCo’s list of 115 verbs to see that establishing a “rule” for a relative-gerund/infinitive sentence would be highly problematic.