Tactical infinity is the thing that separates RPGs from wargames or board games where you might still be in control of a personal avatar. The lack of it is why HeroQuest and Gloomhaven are not RPGs (even if you do improvisational playacting and get "into character" while playing them).
Think of it this way: imagine a character standing in a dungeon corridor. It doesn't much matter whether the character is Roquhan the Bold (a fully-realized and fleshed-out personality, a warrior of renown with a 10-page tragic backstory and aspirations of revenge); Fighter #3 with 8 hp and Str 16; or a perfectly blank cipher. The character is in a dungeon corridor; you're in control of them. What do you do?
Making that decision — taking action — is roleplaying. It's not just some part of the game that you can take or leave, it is the game. It's playing the role, it's roleplaying. And what makes it roleplaying is precisely the fact that your choices are unbounded (or rather, bounded only by the specifics of the situation — by the fictional positioning). Do you go left? Go right? Listen? Sniff? Rap on the walls and floors in search of secret passages? Try to figure out how to do the same on the ceiling? Rummage through your possessions, hoping something will give you an idea? Make loud noises to attract wandering monsters to interrogate? Bellow out Randy Travis songs at the top of your lungs in hopes of frightening monsters away? Something else? The possibilities are functionally infinite in a roleplaying game; they are not infinite in a board game.
In HeroQuest, once you've fought all the monsters and searched for traps and treasure, there's nothing in the game to do but move on. You can't ever try to negotiate with the monsters or try something the rules don't cover. If you and your fellow HeroQuest players do make that provision — if you do add tactical infinity to the game — you're not really playing HeroQuest anymore, you're playing an RPG that you've made out of the (respectably conducive) HeroQuest board, pieces, and maybe game mechanics.
(And hopefully nobody gets too hung up on the illustrative dungeon setting; it's just a simple example that demonstrates the point. The concept is perfectly transferable to other settings and scenarios.)