To be honest I've never ever had my tickets checked on a Thameslink train and I use them regularly, but maybe its more of a MML thing than an East Coast Main Line thing.
WMT/LNWR I do agree, tickets are not check regularly at all and I use them pretty much everyday but recently they have been getting better I think.
Aren't most Thameslink stations gated though ? So if you've not got a valid ticket you can't get through the gateline - or have to work around it. Even interchange onto the Underground is nearly always through a gateline now.