I practiced muay thai for a year and my teacher made it clear we would train all along bare feet on the hard ground.
Of course I had feet injuries after repeatedly kicking the mitts. At first, I thought I would hold on and eventually my feet would get used to it.
But it didn't get better and honestly, this is one of the reasons why I didn't follow up.
Would you recommend training on mats or is training on the hard ground really a thing ?
I see no trouble training pure striking on a hard floor. It's also not clear that the floor was the cause of your injury--you say it is from hitting pads.
If throws, clinch, or takedowns are even a possibility--as they generally should be--then mats make more sense, but that doesn't seem to be the issue here.
I would not recommend staying in any school, regardless of style, that insists on doing something that results in students being injured; this is a sure sign of a McDojo.
That said, what is the hard floor? Is it a nice polished wooden sprung floor? Is it bare weathered concrete in the parking lot? There is a huge difference between those and anything in between. Some hard floors are fine to train on, others are not.
We've moved our hap ki do dojang from a place with mats to a place with super flooring as the floor and as yet there have been no feet injuries. We put mats in place when we're throwing and doing take downs. I agree that an instructor who pushes you through injury is a danger.
Would you recommend training on mats or is training on the hard ground really a thing ?
I would really recommend training on mats, no matter the art you do.
I used to train on tiled floors, so we were very careful performing stunts like takedowns and jumping/flying kicks. In Taekwon-do the pattern Choong Moo has a move to jump and spin 360 degrees in the air and land with a knife-hand guarding block on an L-stance. This is not my favourite move to perform on a hard surface!
Landing hard on hard surfaces will easily hurt the knee if not done properly. So train on mats if you can, but if you can't, be careful not to hurt yourself.
As a general rule, I've learned to not do any hard or explosive training on hard floor that doesn't reduce the impact. Even something as small as simple as sprinting is now done on a track where the track absorbs some of the harsh impact. My father used to train on hard floors and now suffers multiple knee problems. What I've learned through hear/say through my mentors in training was that training on hard floor training is a no-go.
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It is really good to train in hard ground.
However, I would say to you not to change the floor drastically Start trainning in good hard floors like said before, and then change to the worse when you get used with it.
