As interesting as minelaying would be to deny an area of space from travel, the basic mechanics of the game with non-persistent items means that not only would you have to have someone hanging out in the instance where you dropped your mine field(s) or they would disappear makes the concept moot.
The only minefields that would be useful would have to be laid inside an area either experiencing an active conflict or soon to expect fighting. Or griefing, I suppose.
Well, my primary line of thinking is simply that regardless of game mechanics, I'd like a minelayer/minesweeper ship just to see what CIG would design as an analogue to modern ship design, just like all the other purpose-intended hulls.
As far as actual game mechanics, I trust that CIG would be able to come up with something that was well-balanced and not just a griefing tool. I can imagine minelayers as being useful for protecting mining and salvage operations. Imagine TEST manages to find an old derelict Bengal wreck out in deep space, but the hull is going to need a good bit of repair work just to get it moved to a safe location. I'd definitely want a minelayer or two to put down a protective screen to prevent incursions while we deploy Crucibles to get the wreck moving under its own power.
Plus, I think people entirely overlooked the mineSWEEPER part of the description - detecting and destroying mines sounds like a pretty cool task in SC. Heck, there's a crappy 2D version of this that has consumed millions of otherwise productive hours worldwide...