People play games with dance pads, or with their feet, or with Guitar Hero instruments, and they have fun doing it, but that doesn’t mean it’s efficient, or optimal, or that those control schemes are “good” for the games they’re using. If your argument is “Controllers are adequate for FPS games”, sure - I don’t think anyone is refuting that point, but that’s not the argument you made - you stated that controllers are good for FPS games, which is a pretty subjective word, but clearly you posted in the right place, because as you can see from all of the replies here, it’s a very unpopular opinion.

Clearly people can play FPS games with controllers. It is an option a lot of people use. However, it’s just the case that an equally skilled player on a controller will lose to a similarly skilled player on M+K. There’ve been numerous attempts at scientific tests to prove this. Here’s one such example. There’s an anecdote that years ago, Microsoft was considering offering cross-platform multiplayer between PC and Xbox, but scrapped the idea when it was discovered that very skilled Halo players using a controller were losing to objectively less skilled players using mouse + keyboard.

Not to pry, but “having fun” is subjective and therefore there is nothing “wrong”. It is up to the subject to decide or feel that something fun is happening.

You are “subjectively right” but you are also “objectively wrong”.

A clear reason is that Aim Assist was implemented to make the player have fun. K&M do not need this support because you can aim very accurately without previous training.

The barrier of entry, as you call it, is reduced artificially for the controller.

But alas, do what is fun for you. There is nothing to prove to anyone in single player games. I play third person (Souls games) games with controller and FPS (Cyberpunk mainly) with k&m.

What inconsistency did I list?

Changing a sensitivity on a mouse is easier than on a controller and generally allows a more fine tuned setting.

Console games usually give you a limited number of options like 1-10, 1-20 etc, these are arbitrarily different on each game.
Ignoring the fact it's easier to even use the menu to get to the sensitivity option and just input a number with the keyboard, you can also calculate the distance you have to move your mouse to make your character turn 360 degrees in one game and then convert that into any other game to have exactly the same, something you cannot do on controller.

Going through the sensitivities for controller is a hell of a lot simpler than going through sensitivities for keyboard and mouse.

Crank it to max, then dial it back until your shots start to land

The title of your post begins as "Controllers are good for FPS games, especially on PC".

Now it's about having fun and a lower barrier of entry, not competitiveness.

It's fine you prefer controller, but you're moving the goalposts here. The title and body of your initial post isn't about having fun, it's about what is "good for fps games." K&M is, I'm sorry to tell you, objectively better in that sense.

Side note, as for your "lower barrier of entry" for a controller part, you also specified from the beginning, "especially on PC". If you're playing on PC specifically, you already have a K&M. A controller is not a lower barrier of entry on that platform, it's an additional purchase vs. something everyone on that platform would already own.

You're using a list of inconsistencies to deny why you are "objectively wrong".

For single player games, sure. For multiplayer games, you will get absolutely wiped by KB+M players and that will not be fun for you.