How right you are. As I'm sure your aware, it's not about signal strength but about the signal to noise ratio especially when the noise is a ghost producing reflection.

Been an electronics engineer and an antenna buff for many decades as a ham radio geek. Once made a 24 foot long yagi for 2 meters like this which freaked my mom out no end. Made the house look like a sailing ship but worked magic. Same typical 13 Db gain.

Low noise amps can help but they won't be much better than the front end of your TV and don't help with reflections. Mostly useful for long transmission lines or feeding several recievers. They won't have a much better signal to noise ratio than the front end of your tv, possibly worse.
And of course 12 Decibels equals a linear gain of 16X.

Got my Digiwave 2190 online Walmart - $40