The only real way of scrutinising people is before they arrive, by requiring them to obtain a visa before travel. But if all the Brits with a criminal record were denied a visa it would probably drastically reduce numbers.
I think they are just getting what they're bound to get when they allow people to arrive unchecked, and as someone else mentions, it ain't just Brits. (Pre-COVID figures suggested that more Brits visit Thailand than any other farang nationality).