So as far as I know the country drawing is not completely random, but somthing like "to pick the same one two times in a row is less likely".
But this would mean that drawing one single country 5 times out of 10 games is as likely as having all countries once or twice? Thus, giving you no information about which country you might get when joining the next game.
I just took a view at my game record and counted how often I had which country. The result (out of 31 games):
6 times France, Turkey
5 times Russia, Italy
4 times England
3 times Germany
2 times Austria
Actually, before I took a closer look at the real numbers, I felt like: Oh Man, how often do I have to be Italy again? Now, seeing that Russia has the same number and France and Turkey are even higher numbers, shows me, that my sense was just wrong.
So, to end this long post, I would love to point that in my eyes there is no need to change the draw system. It would be mad to know "oh, I can join the high pot game now as it is very likely to draw my favorite country".
And with another system I might be Austria more often, which noone should wish to happen ;-)