Most people just seem to instantly go delving into programs trying to make a game in the hope they make something great. I'm not saying it's a bad thing to do, but how many games have been developed like that?

I will reverse your question. How many games have you finished while "sitting with music on"? :D It's easy to point out problems of the "start with programming" method, but in practice, how many times which method worked?

When I look at my games, I truly regret "thinking too much", so far it NEVER paid off :D And my best games were the ones that I spend minimum to none thinking beforehead (dunno why, I don't want to create a theory here, but that are the facts, in my case at least). Also, frequently this overthinking/overdesign lead to a worse game in the end...

My tip would be: impose on yourself some sort of limitations (especially time) and do not be afraid to use a healthy dose of cloning (so far none my games suffered from being "too much of a clone" while some do suffered greatly from being "too original" - sorry, pure originality sounds great for marketing purpose only, but it will rarely make a fun game)

I generally spend years designing hobbie projects before writing a single line of code... and months designing after my first prototype before I even get to actual development...
It's a hobby. I can afford the time, and it makes for a better design.

Case in point, I've been working for years on my current project, and all I have to show for is two prototypes made in Dartlang (the game is actually made in Unity). But the designs... oh boy... man... have I got a lot of documentation (still sorting out through some of it as I keep simplifying the core concepts to their bare essence).

Wow... Years?

That is dedication. I can understand wanting to design perfectly, but a lot of people would lose interest within a few months.

Years is hardly impressive. Given these are hobby projects that require hundreds to thousands of hours to make and that I hardly get more than 0,5h daily on average, and that I have several projects at once (knowing fully the majority won't make it into production) this all makes sense.

Perhaps the average project scope is slightly larger than what you may have in mind however...
For example, I have been working on the same rpg 10 years and spent the last 4-5 years working on a 4X. Of course there were others along the way but most did not stick or were spinoffs (fighting game built from the 4x battle simulator for example which required minimal redesign for UI).