I strongly suspect budget is a reason certain events are not shown. People underestimate the rate of good CGI, which is insanely expensive, and this show has very impressive CGI. I don't mean to harp on the horrible opener that skipped the Walkers, but they obviously didn't have the budget there (all spent on the dragons?), so instead, we only heard swords clashing with a blackened screen to suggest there was a skirmish. Horrible choice to open a season-- and it came off as a cheap cop-out, not a creative choice.
I don't think they need to go about Dany's 3 armies in the same way it's written in the book(s). They've certainly taken creative liberties throughout the seasons, so why not here? They could have the concept of 3 armies at her service by creative means that would not prolong, nor drag her story down, nor devote too much time to it. Dany's already becoming a threat, a force to be reckoned with in the West through word, to the point that some feel she needs to be assassinated: So a simple story of certain armies willing to come to her aid because of her legendary dragons would work for me. I feel as if they're diminishing her status by having her just "buy" an army.