Several reasons:
I have entrance onto some decent green lanes within less than 15 minutes from me whereas the plain, or at least the nearest to where I can ride on it, is over 30 mins away
I'm never entirely sure which parts are legal to ride and whether they are open on the particular day/time I get there
When wet, which is quite often here in the UK, the chalk surfaces on the plain are very, very slippery
I prefer the nadgery 'proper' green lanes rather than the wide open tracks that much, but not all, of the plain consists of
Main reason is definitely the first, convenience, I'm sure if I had access to the plain ten minutes from me I would right it much more often. Good luck with your new riding adventure, I'm sure you'll enjoy it