
Adjoint |

I allowed homebrew spells in my games, as long as I get to review them beforehand. However In particular, I allowed for the spells gained for free at the level ups to be hhomebrew. It ended up to be the only opportunity when my players creted new spells, they didn't use spell research option.
It didn't affect the game much. The players had some custom spells that matched their theme or particular needs (for example one had a version of Aggresive Thundercloud which was more like miniature sandstorm, and another created some spells to deal nonlethal damage, for his character didn't want to deal lethal damage).

Tsukiyo |

I used spell research rules for my trickery witch to learn (the off list) invisibility. By that point, she already had mislead from her patron spells, so it didn't seem OP to reverse engineer that spell into the less powerful invisibility.
Were I GMing, I'd certainly allow players to use spell research to grab off list spells assuming they can justify it to some degree and its not just a naked power grab.
Have never felt the need to homebrew spells, as PF1 already provides so many.

Bjørn Røyrvik |
I've allowed it, but it has not been used more than a couple of times, to moderate. Most important was a 6th level variant of Reincarnate that functioned along the lines of Resurrection (allowing those slain by death effects) to return.
More impactful has been spells from previous editions that have been updated and introduced. Stuff like Pierce Any Shield, Immunity to Magic Weapons, and Counterspell Immunity can really alter the game.

ErichAD |

I've allowed it. I don't let the players dictate the exact mechanical effect of the spell, just what they want it to do narratively. I also allow players to research higher level versions of spells to get a more liberal interpretation of the spell's effect. For example, if someone wants to use a floating disk as an impenetrable portable horizontally aligned wall of force, they can research that as a new spell.
I'm more inclined to allow players to research rituals rather than regular spells. Player spell research has mostly been pointed toward dealing with something specific to the game world, so the result has generally been positive. Refusing to allow the players to dictate specific mechanical effects seems to be enough to prevent power grabs.