The built-in mics are generally fine, though you can't deny their not as large as good external mics. This makes the mic's diaphragm smaller, but this is not the point.
Examples: A singer on stage has a mic right up to their mouth. A news reporter at the studio has the mic clipped to their shirt getting as close to their mouth (the audio source) as possible. A person making a speech or responding to questions during a press conference from a podium has a bunch of mics at the podium, near the audio source. Shotgun mics on booms pointed at the person speaking. The list of examples is endless.
In each of these examples, the camera is further away. It has the ability to zoom using optics. The only place I know if that has some sort of "zoom mic" is a parabolic mic used during US football games from the sidelines - and they won't fit in a camera very well.
So when the camera's built-in mics are in the right place, the video framing usually won't be desirable... but when the video/image framing looks right, the built-in mics can't be in the right place for the audio... hence external mics or external recorders which allow the camera to be in the right place for video and the mics to be placed independently for audio.
If there was a consumer grade camcorder in your price range that was "better than most out there" then the professionals would already be using it. They don't like having to lug extra equipment around to make sure the audio and video are good for broadcast... one less thing to worry about and less equipment to buy, maintain and all that. So, they's already be using "it". But "it" does not exist so they keep doing what they are doing... separate, external, mic.
The *only* two times I have found a camcorder or camera's built-in mics are in the right place and the video framing is fine is when the person speaking is about 5 feet away from the camera speaking to the mic - or during a live concert (manual audio gain control is in use), the camera is in the audio "sweep spot" of the venue and there is no panning. But this is not how all video is captured which is why we all suggest the external mic option.
The least expensive camcorder of which I an aware with a mic jack is the Canon HF R500. Action cams are not "normal camcorders - neither are still image cameras that happen to capture video as a convenience feature.