I agree strongly. Since mines cannot be:
1) Voluntarily scuttled, destroyed, manually detonated, or in any way removed by the faction that put them there in the first place
2) Cleared, without throwing your fleet into them
Also, since mines are usually autocast, (at least by Vasari, anyway) they tend to accumulate terrifyingly quickly.
As has been pointed out, this causes a not insignificant drain on computing resources, as the number of objects in the game to be updated and rendered is only increasing.
As an experiment, I made 20 Ruiners, and only those ships, and took them into a system with a fleet that had no fewer than four capitol ships, 15 carriers, 20 light frigates, at least a dozen support craft, and a partridge in a pear tree. By simply moving the minelayers back and forth through the enemy fleet, I was able to destroy it almost entirely.
I don't think I'd be the first nor the last to come to the conclusion that in their current manifestation, mines are incredibly gameplay destabilising.
Mines need to be limited in some way. Whether they decay over time, or whether there can only be a certain number in a gravity well, or whether the minelaying ship in question needs to re-energise the mines periodically to prevent them from becoming inert: some mechanism needs to be introduced to make them not pile up indefinitely. From a computation as well as a gameplay perspecive, this is a show-stopper.
From a strategic and tactical point of view, I will also join the chorus of those people who are clamouring for mine-sweeping ships.
I don't think mines are a bad idea per se - I just feel that in their present state, they will do the game no favours.