I don't think regiments themselves can be purely blamed for killing the game, considering that they are the base of the game and one of the main reasons for its success. While public games are fun, they are easy to get bored of and without regiments the game certainly couldn't be as successful as it has been.
I think the game is just dying because it is old and every great game (apart from Rome: Total War) goes through this. No point blaming regiments, considering a lot of people purchased the game to join them.