Quoted:
Thicker doesn't really mean anything as far as real-world performance goes.  Some guys will tell you it's "more rigid", and "won't bend" etc. etc.

Bent recoil lugs are very rare, especially in properly fitting or bedded stocks.  I might consider a .250" lug for a large magnum caliber (300 and 338 ultra mags, lapua mag etc.), but that's still just paranoia.

Because it's sandwiched between the barrel and receiver, what IS important is lug squareness.  The factory lugs aren't always as square as a guy would like, but a couple quick passes on a surface grinder will ensure they are.


Edit: Bedding in the recoil lug pocket is a quick fix or assurance to keep from having to do a full bedding job.  The idea is that you're getting 100% lug contact with the stock.  The lug is what should transfer the recoil from firing to the stock.  If the lug abutment in the stock isn't square or you're not getting solid contact with it, you can get accuracy issues.  If your lug isn't touching the stock at all, the rear action screw is liable to transfer that energy to the stock.  If you ever see a wooden stock that has a crack in the tang, it's a tell-tale sign that the rear action screw is contacting the stock and acting as the recoil lug.