I had initially thought along the lines of trained soldiers becoming trainers rather than just any soldier doing it. I did not mention it as there are enough people who are resistant to change already without giving them something to shoot down without further thought.
This would further exacerbate the problem of not getting new trainers. Trained soldiers are sent to the front. Now to get a trainer you'd have to stop all your military buildings from getting promoted soldiers. A big hassle of micromanagement for a skillled player, an insurmontable obstacle for an inexperienced one.
And answering legitimate criticism with complaints about prejudice won't help your case.
Just a quick thought of an alternative way to create trainers:
As already mentioned currently one needs to have the corresponding wares (weapons) for a trainer in the same warehouse. A worker picks them, gets a trainer and walks to the trainingsite which requested a trainer.
To avoid the problem of having both wares for a trainer in the same warehouse I could imagine to let the trainingsite create the trainer. If no trainer is available the trainingsite will request a carrier and the needed wares. When all of them are there the trainer is created, just like in a warehouse. Even if at the time of the request none of the needed weapons/armour are available they will be made and delivered finally. This could take a while, depending on the requests for weapons of other buildings, but eventually one would get a trainer. This works without the need to micromanage the warehouses/barracks/other trainingsites to make the weapons available.
That's actually a great idea. It would fix the micromanagement issue and it would be friendly to new players. I support the idea (which I wouldn't do if I was resistant to change and looking for something to shoot down)
EDIT: this would also let us take in tinker's idea of trainers needing weapons without creating micromanagement hassle. All it would take would be to define trainers levels. So a level 1 trainer would need a level 1 weapoon and armor and could train to attack 1 and defence 1, a level 2 trainer would be made by givving a level 2 weapon and armor to a level 1 trainer and would train up to level 2...
Not only it would work, but if we give everyone just level 0 trainers for start, it may help with balance. Now the first to produce a full set of weapons has a huge early game advantage. If we make this change, one would need to produce 2 sets of weapons and one of armor before getting an effective soldier, which would severely cramp the combos to get a supersoldier in early game. It encourages better the making of a full economy rather than finding shortcuts. I now also support this proposal