What are the drawbacks to standardizing languages?

You lose linguistic diversity, as the dialects gradually die out, or at least are marginalised. You may not may not care about linguistic diversity, of course.

You lose ways of saying things that are specific to non-standard dialects. Cretan dialect for example has a distinct word for “trickle”. (To my annoyance, I don’t remember it.) Standard Greek only has “run”, a verb which applies equally to dripping, trickling, and leaking. Pontic Greek works on animacy, not gender. Tsakonian has some very archaic usage of the participle, which end up sounding closer to English than Modern Greek (he started barking αρχίνιε κχαούντα; I am seeing έννι ορού).

You lose the cultural associations that the dialects expressed; you sacrifice the distinct cultures conveyed by the dialects in favour of the standard.

If your language is moribund and there are still native speakers, standardising languages turns out not to be a good idea. Oh sure, you have limited resources to promulgate the language, and they’re more efficiently expended through using only one standard form. But when the standard form is not what the native speakers of the language actually speak, all you’ve ended up doing is alienating those speakers from the media you use. That’s what happened with Gaelic for example: the remaining speakers out in the Hebrides felt even worse about the language they spoke, because it didn’t match what BBC Alba was broadcasting.

If the standard is not anyone’s native dialect, you’re going to have some disruption while people learn the new standard, and get used to it. In fact, if the standard is not preexisting, you’re going to have some disruption while people flesh it out and elaborate it. And they may do a bad job of it.

If the standard is someone’s native dialect, you’re going to have enduring resentment from speakers of the dialects which have missed out.