This was by design. Both Philbin and Gase prefer an offense based on short timing route passes, and they both said that these passes will mostly replace the running game. Both coaches also seem to prefer throwing to the RB rather than actually running the ball. And, they both placed little importance on the o-line's run-blocking ability. To be fair, once in a while they did attempt to establish a running game, but because they place too little emphasis on it they usually weren't very consistent. For instance, if Miami actually had a lead late in the game with more than a few minutes to go, there's no way that they'd be able to keep the ball on the ground and run out the clock; neither Philbin nor Gase can/want to play that style of football.
There was one series of plays by Philbin's team that I'll never forget... although I can't remember the opponent or year. Miami had the ball at (or just inside) the 10 for a 1st and Goal. On 4th down there was a defensive penalty and Miami received 4 more downs. So, Miami ran 8 plays starting from just inside the 10 yard line, and EVERY SINGLE PLAY was a pass. Not one stinkin' run. Needless to say, Miami never scored and the opponent took over the ball. How can you NOT at least try to pound the ball into the end zone? Did Philbin hate the running game that much, or did he realize that his "finesse" o-line would never be able to overpower the d-line? Either way, that series proved to me what I already knew... that Philbin had no business being a Head Coach.
Well yes and no. Yes, they did want the short rhythm pass plays that essentially act as a ball control offense in place of running plays. That is all very true.
But they wanted to run more stretch zone plays in the run game, and relied on OL who were supposed to be proficient at it. The problem was that we never had the OL to make it work. So, we couldn't succeed with those run plays. Defenses decided that the way to stop that offense was to clamp down on those short routes, push the pass rush, and dare us to throw long. Our OL also was nowhere near good enough to give us the protection to keep a QB upright long enough for those deep routes to develop. Thus, those short passing plays were ALL we had, and very easy to stop.
Where actual run plays come in, is that they let the OL be the attacker, and the OL begin to physically wear down the DL and LB. This shows up in the 4th quarter, as those DL are less fresh, and cannot generate the same pass rush, particularly interior pass rush. The LB are less quick to fill and chase, leading to more often chunk yardage. The offense has an easier time converting 3rd downs and keeping drives alive. Gase went so far as to publicly admit that he has his staff keep him committed to calling run plays for Ajayi while he was here, as we were seeing a lot of success in the 4th quarter from this whenever our OL matched up well enough to generate enough run lanes to make it feasible. When we got rid of Ajayi, we stopped winning those close games and that 4th quarter effect disappeared.
Now with a better run blocking OL, we can spring Drake past the LB often enough to make it work again. The run game becomes a viable option.
It's as much that Philbin and Gase were OK with scrapping the run in favor of the short pass, because they both understood the consequences. IMHO, it's more that they both saw the short passing game as a viable substitute for the ball control offense when and if we could run it effectively. Subtle difference, to be sure, but a meaningful distinction because we built our offense to make that short passing game work--as you so correctly pointed out--and our OL simply couldn't run block worth a dang. So, when it the short rhythm passing game didn't work, we had no options.
This basic failure is the main reason we could never implement the hurry up offense both coaches wanted. We simply couldn't pass block for the deep pass nor could we run block, so teams just clamped down on those short routes daring us to throw long or run at them … and we couldn't. All the hurry up did in those situations was make us punt faster and put more pressure on our own defense.
With a viable run blocking OL, we have the ability to run at those defenses clamping down on the rhythm passing game, and physically wear them down by the 4th quarter. With improved pass protection and a 3rd down back (Ballage), plus two TE's (Smythe to block and Gesicki as a safety blanket, seam threat, and chain mover) we are far better equipped personnel-wise to handle blitzes and provide protection for those deeper routes.
Finally, we will not be so one-dimensional. This should allow us to get a lot more plays that look easy. They're not easy, but we can finally adapt to the defense and exploit matchups, which we couldn't do in years past with no TE's, no ability to open up run lanes, and some of the worst pass protection in the history of the NFL. In an NFL where almost every defense is built for speed with small safety-like LB's, all small quick gap penetrating DT's, and CB's who cannot hold up against run defense, being able to impose your will has even more value. Wearing down defenses--particularly good ones--becomes even more valuable. Letting your OL fire off the line and become the aggressors is also a huge advantage psychologically. With a big strong G like Jesse Davis, that's possible. With a C that is more effective at the point of attack like Kilgore, it is helpful. With a dominant G like Sitton, it makes having a run dimension every game realistic. This is a big change, and one I've been begging to happen since forever. Our run game is extremely overdue. Just my $0.02.
