I think representing GB can be positive if you are top 250 in terms of WC entry to Wimbie/ 2x ATP or WTA. Certainly, more opportunity than representing Greece would give, and probably Spain given the competition for WC in that country. A Wimbie WC itself is a big pay day that makes a big difference to the balance sheet for cash strapped players.
But below this, I suspect the case is less obvious-no great number of challengers/futures to utilize any more, and I don't think the LTA is very generous beyond supplying facilities.
I don't think Ollie going Greek has anything to do with the LTA being meanies.
There's a good chance that he'll make their DC team in the recent future, which was extremely unlikely while he was playing for GBR.
It's also possible that he'll receive better funding there. Of course there's no comparison between the wealths of the LTA and the Greek body, but out here he must be behind loads of people in the priority list (to be fair, that's quite right since you can't fund everyone). Maybe he'll be better off in Greece once he gets a few points?