They promised every race (not class) to be in the 5e PHB after many fans cried about the gnome race no one even plays.
They did actually say something to the effect of "every PHB class will be present
in some form," that may not have been the exact wording but they definitely went out of their way to give the impression that if X was a default, first-book-set option in the past, you'd get it. The general failure to produce an actually Warlord-like option was a major point of consternation at release. Particularly because the people who were pleased with 5e kept giving delaying excuse after delaying excuse after delaying excuse. "It'll show up in a packet soon. Don't worry about it." "They'll include the Warlord Fighter and the tactical combat rules in the final packet, you'll see." "They just saved that stuff for later because those designs are harder! It'll be in the PHB when it's published." "Oh, come on, you can't expect them to include EVERYTHING in the PHB. Give it a couple years."
Yes, I
literally did have someone (usually several people) tell me
each and every one of those excuses, without exceptions. Including that last one. I had someone
explicitly tell me that I couldn't form a valid opinion about whether 5e was good and actually fulfilling promises like this unless I gave it
at least 2-3 years first. After having already waited through nearly three years of playtest. Yeah, I was...not particularly enthusiastic about that argument, as you might guess.
All the new to 4e classes are doable as new classes in 5e. The issue is that the designers decided early that they weren't adding new classes to the PHB that weren't in the 3e PHB besides Warlock. All new classes would be setting only and due to the slooooow publishing schedule of 5e, only one was created.
For a definition of "doable" so weak and watered-down it would fairly resemble certain popular beers, sure.
And no, they
didn't decide those things early on--or else they did so and never told anyone. As an example, Mearls
explicitly tweeted that there WOULD be martial healing in 5e, and if players didn't like that, they could simply choose not to play those options (or, if DM, choose not to allow those options). And y'know what came of it?
Diddly-squat.