The gold mine is very worth it. I admit it didn't seem worth it when I did the maths like you - the resources to build one mine versus having only 300 ore in it seemed very strange, and then when you look down the production chain and don't get very much out of the other end I was a bit wtf too?
The thing is the game changes as you go up the levels. By the time you start playing with gold you should be clearing out the last two zones - clearing these zones takes a LOT of time. During that time you aren't spending very much on resources - You have to replace iron and coal mines, but your wood and stone income are much more than the cost of these mine replacements. You will also do a lot of building upgrades that use wood and stone until you hit the upgrades that cost gold. And there's the hint - eventually you start needing gold - a LOT of gold - for everything.
Lets put it like this, even at the ridiculous cost per gold mine I always have 2 and try and aim for 3 gold mines continually working as much as possible.
I keep the coinage and smelter and mines buffed as much as possible. The coinage is the most important because of the maths, but I always try and keep them all buffed always. I've just bought my 3rd explorer which is crazy at 1600 gold - imagine how many resources 1600 gold would buy on the market - but the point is none of the earlier resources are much use to me any more, and they come in faster than I need anyway. I just hit level 31 about half an hour ago and now it seems that I need explorers more than ever before for expert resources so maybe not so crazy buying a 3rd explorer for 1600 ?
Anyway going back to the original question - at some point you will have enough resources spare to continually build gold mines with no financial pain and you should do so as quickly as possible when you get to that stage in my opinion. I'm now about spend all my gold income on upgrades where it costs several hundred gold per upgrade. Also fyi there is no option to buy a 4th explorer atm at any price.
The game changes the higher you get, you are just close to a changeover point where your priorities change.
Also you don't have to rebuild the gold smelter or coinage which is one small relief![]()