If these do not initiate the movement (aided by some forearm rotation which only aids and does not replace hand action) the hand is forced to stiffen like crazy.
No, it doesn't. If you have active fingers, and feel the fingers, that's perfectly enough for getting sound. The part where you no longer gets tired varies from person to person. Some works like Chopin studies - once you know then enough, you will stop feeling tired - with some help of slow practicing, and more effective movements.
For others they might need to vary the position of the arm and wrist. The tiring part is when it becomes static, and not the movement itself. If you simply rotate the arm in the air, you will be able to do it long enough without getting tired.
I spent years trying in vain to understand what people were on about with rotation, all to no avail. My tremolos were pathetic. Finally, I can do the ones in the Liszt arrangement of Wagner's Liebestod with speed and ease- with only smallish amount of rotatation that are not close to enough to account for the movement of the keys. Only getting the fingers moving eliminated the need to brace things. Rotation and finger movement need to sometimes be worked on individually and sometimes combined.
It's perfectly possible to only rotate tremolos. Most people will probably find easier ways to do it, by, again, active fingers. I feel the need to point out that active and moving isn't the same thing.
If you move your arm so that the natural weight is on the key, you will be able to only rotate.
Ultimately, I use vastly more finger movement than rotation to produce speed and sound. Rotation is just what makes sure I'm not locked into position- not a literal instigator of the primary energy behind each key depression.
I used vastly more rotation than fingers for my first 4 years of playing. I managed to play both waldstein, the mephisto waltz and the symphonic studies.
Now I have a new teacher, and I use more fingers, but the arm (or rather the weight of it) is still a far more than only fingers.
Whatever all the standard methods might claim, without notable finger movement, rotation is both slow and laboured and can cause considerable stiffness in the hand. While rotation is something you cannot afford to eliminate, neither is it something that can credibly account for anything more than a particular component of what is required to eliminate bracing.
If you get stiff from rotation, you simply do it wrong. The whole point it to release tension from the arm, and let the weight do the work.
I know many pianists from my country who basically only use the weight of the arm, and "Active" finger. They are able to play things that many pianists has to work for ages to learn - and they aren't even 20.