I think it will cause you problems on some games if you try to only use one coin button... if I remember correctly beat-em-ups like TMNT, X-Men, Simpsons, etc each had their own coin slot and auto started the character once a coin goes in. I've had multiple gaming sessions where 2-3 people would be playing, a new person would join up to play and hit the coin button a ton of times for their player, and then end up leaving and it was a huge pain because the player wouldn't die until all of the coins they entered were used up. If you had MAME accept one coin push to activate all 4 coin slots, you would potentially be starting all 4 players at once for games like this.
One option would be using "shift" buttons where you could hold p1's button while pushing the coin button to give p1 a coin, hold p2's button while pushing the coin button to give p2 a coin, etc.