Not downvoting and not leaving negative comments to discourage non-hacky answers would be a good way to improve answer quality.
In my view, conventional solutions using existing, well-established tools and methods are implicitly verified, and so discouraging them discourages known working solutions, attracting a higher proportion of unverified answers to begin with. E.g. with the ant example from the OP, conventional solution is identify the type of ant, remove food sources, use appropriate baits/pesticides, call exterminator for larger infestations. That works. Discouraging this encourages unverifiable, or at least less effective, things like "ants don't like cucumbers / cinnamon / peppermint oil / etc.".
Often times the highest quality answer is an easy conventional solution that the OP was not aware of for whatever reason, while the hacks are frequently misguided, unsafe, inconvenient, or otherwise less than ideal.
One recent example is How can I remove ants from my laptop keyboard?, for which the OP actually found the best solution in chat (just use ant baits) and was then hesitant to self answer because it wasn't hacky enough:
OP: I ended up following ton.yeung's advice in a chat room and got rid of them just fine, now I have no idea which answer to accept since I didn't try any.
Person: cw self answer quoting the chat advice
OP: It's not really a hack, just bought a box of ant thingy and left it on the table.
This isn't an issue with the OP, but rather a bigger picture issue resulting from the actual best answers being discouraged because they aren't hacks. The exchange quoted above is a big time red flag. Many, if not most, of the questions here are answerable with existing tools that are designed specifically for the task being asked about. To not recommend such tools (tools that were generally created after much struggle by others in the past with the same problem) is lower quality advice, by nature; such answers do not build on the experiences of the past.
I acknowledge that the question of whether or not "conventional" answers are acceptable is controversial. I also acknowledge that even the definition of "conventional" is relative and up in the air. Such discussions can be readily found on meta and I understand them. Regardless, the fact is that discouraging "conventional" answers places a constraint on many (not all) questions that leads to low quality hack-style answers.
It must be accepted that just because it is a hack doesn't mean it's a high quality solution to a problem. That isn't necessarily bad, per se, it just means that if conventional answers are to continue to be discouraged, then lower quality solutions must be accepted as a necessary consequence. Which is fine, if that's the goal of the site.