As a relative beginner, I think it's funny that you say "they could’ve just said 蕎麦屋 rather than そば屋", since I can actually read the latter, but not the former. And my guess is that's why they write in kana; to be easier for people who don't know all their kanji.

Wife (native speaker)'s thoughts: lots of strokes, harder to read on small signs, etc. 薔薇 for rose is something that's almost never written. Another thought is older or variant characters that are now replaced by simpler ones in some cases just didn't catch on after. This is just her spitballing ideas and not researched.

Japanese learn a lot of these so most adults can read them.

There are certain words that technically have a kanji spelling, but are usually writen in kana even outside of signage. I think it's mostly words that would have been important to historically less-educated people, so a lot of them are foods. It's probably not a coincidence that it's not uncommon for women's names to be written wholly or partially in kana (e.g. かおり, このみ), who traditionally are the ones to buy the groceries.

On top of that, for signage specifically it's lot easier to read things like そば, ラーメン and たこやき/たこ焼き from a distance than 蕎麦, 拉麺 and 蛸焼き.

I was told by a local that, mirroring what other people are saying, it’s so the menu is easier to read and readable by more people.

In the past, Japanese literacy was lower and immigrants also had difficulty reading Kanji (especially Chinese immigrant, since Japanese Kanji is often altered in form and sound when referring to the same thing).

Japanese restaurants mostly keep doing it out of tradition rather than necessity.

(Running counter to this, some Japanese restaurants also use the outdated Yamato style of writing for traditional and aesthetical reasons. Even locals sometimes have trouble reading those character and its use is usually relegated to the shop’s name.)

Kana means chicken in Finnish.