At all is a Negative Polarity Item (NPI). That means it is one of a long list of English words, phrases, idioms, and constructions that can only occur grammatically in a Negative environment.
Rather than being "awkward" or "ugly" (which are esthetic judgements and not grammar),
- *That makes sense to me at all.
is simply ungrammatical, since there is no negation present to license the use of at all.
So it's incongruous here; what could it possibly add to the meaning in such an environment?
In a grammatical sentence, say,
- That doesn't make sense to me at all.
- That makes no sense to me at all.
- Nobody understands that at all.
at all functions as an intensifier of the negation, meaning something like 'in even the most insignificant manner'. But without a negative environment to license it, at all makes no sense at all.
There's a lot more to say about Negation and Negative Polarity, but this is a very simple case.
Edit: Specifically, just to get it all on the record,
for the future, here's the list of Negative Triggers from
(If-Clauses fall under "III. Hypothetical Clauses)
- NPIs are illustrated here by the prototype English Negative Polarity Item any.
- *A asterisk before an sentence means (that) the sentence is ungrammatical.
- Parentheses indicate optional material (that) one can either omit or include.
The first few sentences give grammatical negatives versus ungrammatical affirmatives. After that you're expected to find your own ungrammatical affirmatives. (It's rather fun, actually; they really sound terrible)
I. Overt negatives:
A. not [w/ NPI clausemate or complement]
*He (did know/knew) anybody.
- He didn't know anybody.
- *He (did claim/claimed) (that) he knew anybody.
- He didn’t claim (that) he knew anybody.
- *He thought (that) he knew anybody.
He didn’t think (that) he knew anybody.
B. Incorporated negatives
I doubt (that) he knows anybody.
- It’s unlikely (that) he knows anybody.
- It’s improbable (that) he knows anybody.
- He dislikes anybody(’s) reminding him.
- He prevented her (from) seeing anyone.
I kept her from telling anybody.
C. Negative frequency adverbs
I seldom/rarely see any of them.
He hardly/scarcely knows anyone.
D. Quantifiers & quantified adverbs
Only Bill did any of the homework.
- Few people see any use for it.
- *A few people see any use for it. (few is negative; a few isn't)
II. Questions (overt and embedded)
- Did you see anybody?
- How does anybody stand this?
- I wonder how anybody stands this.
III. Hypothetical clauses.
- Tell me if you see anyone.
- He asked whether I saw anyone.
- Tell me whatever anybody says.
- Check the list again, lest we forget anyone.
- I’ll read it aloud, unless anyone objects.
IV. Comparatives, superlatives, etc.
- There’s more/less here than anybody knew.
- He prefers beer to any other drink.
- He’d rather die than hurt anyone.
- He’s as good as anyone expected.
- He’s the fastest one (that) anybody knows of.
- I saw him before anybody (did).
- I’m surprised (that) he knows anybody.
- It’s too dark to recognize anything.
- He left without anybody noticing (it).
- That’s hard/tough for anybody to do.