I checked more than a dozen English usage and style guides from the past 100 years and found two treatments of simply that seriously discuss the merits of restricting its use. From Eric Partridge, Usage and Abusage, revised edition (1957):
simply should, in many contexts be avoided in the sense of merely (as in 'He is simply careless'), for it often sets up an ambiguity. Note, too, that 'He spoke simply' = 'in a simple, unaffected, sincere manner', whereas 'He simply spoke' = ''He only spoke; he spoke but did not act, sing, etc. etc.' As an intensive, simply is familiar English —not quite reprehensible, but to be avoided in good writing or dignified speech; 'simply too lovely for words' may be amusing, but it is also trivial.
From Bergen Evans & Cornelia Evans, A Dictionary of Contemporary English (1957):
simply conveys several ideas and needs to be used carefully to avoid ambiguity. Basically it means in a simple manner [example omitted], plainly, unaffectedly [example omitted], artlessly [example omitted].
Three further uses need to be handled with care. Simply may mean merely, only (I was simply trying to keep you you out of trouble), but it may also mean unwisely, foolishly (Simple Simon has become a symbol of men who who behave simply). This last use is now obsolete. Or simply can, and in colloquial use as a vague intensive all too often does, mean absolutely (She looked simply lovely). This is one of those terms which may seem trivial in writing but which its meaning indicated by the proper emphasis, can be quite meaningful.
After 1957, however, I don't find any mention of simply except glancingly by Barbara Wallraff in Word Court (2000), where a New York Times reader argues that it is a superfluous emphasis word in the phrase "simply and more clearly." But in addressing it as part of a wall of complaining sound from readers about modifiers that may or may not be superfluous, Wallraff quickly loses track of it in the mass of examples. At least I think she does. An alternative theory is that she slyly dismisses such criticism by using simply in the disapproved way in the final sentence of her comment:
But surely our linguistic pockets are deep enough for us to spend a few words frivolously, on things beyond the bare necessities—because these things may bring our listeners or our readers closer to us, or simply because it pleases us to spend them.
The overwhelming majority of style and usage guides since 1957 don't address the question of simply at all. From this profound silence, I infer that at some point after 1957—perhaps in 1958—idiomatic usage of simply in the sense of "only" or "merely" became so commonplace that people in the style and usage game stopped worrying about whether using it in that way would doom listeners and readers to needless struggles with ambiguity.
The concerns that Partridge and Evans & Evans expressed about simply do not seem to trouble their present-day counterparts. Today, you can use simply to mean "in a simple way" or you can use it to mean "merely" or you can use it to mean "absolutely"—and in each instance, practically no one will flinch at the informality of the usage, and almost everyone will follow your meaning unerringly.