I think that pbp is an ideal medium for sandbox-style games, as long as you have player buy-in for the kind of game you'd like to run. The slower pace allows Referees to adjust to changing goals, and the ability to create multiple threads allows you to run large stables of adventurers that split off and tackle different objectives. I've run multiple year+ long sandbox games successfully.
That's interesting, and it reveals that there's a trick to it. Good to know that it can be done, and done well.
Perhaps it's that I am only running 5e D&D, and published material at that. While I like to think that I improve on the material somewhat, it obviously has its flaws. Maybe that's part of it.
I find that whenever I give more than two very clear choices, the whole game grinds to a halt. Open ended "what do you want to do now?" almost never works out (as far as flow goes).
Don't any of my players worry, though! Me discussing my thoughts on the limitations of the form does not mean that I'm unsatisfied with PBP or have any thoughts of quitting. It's too good a chance for me to immerse myself in storytelling, which I have a great passion for.
Plus, I get to tell people that I'm currently running SEVEN D&D games. (6 PBP and 1 IRL game). Makes me sound like an overachieving (read: crazy) DM, which I probably am.