Your video is set to private otherwise I'd love to see your testing. I'm not sure obsolete is the right word but severely underpowered and far too niche would probably work better. I think there is a relatively simple way to fix them and it all lies on their mech units dying forever.
IMO anything have no chance of injury is a horrible mechanic. It's basically guaranteeing your fate. I feel as though the decs feel similarly considering the recent changes to the undead having a base 30% chance of reviving as well as the skills that allow you to revive undead in combat and survivors stay in your army. So how do we do something similar while keeping to the theme of dwarves? Well first let's see what the theme is by starting with what it's not.
Dwarves are not humans, they are not able to be revived all of the time consistently, they do not do consistent damage, they do not have fairly simple and boring abilities.
Dwarves are not the lich, they are not cheap, they are not plentiful, you do not sacrifice them or even consider doing so. They do not overwelm in numbers.
Dwarves are power. They are small, few, yet strong and entirely based on burst damage. They are expensive but well worth it. They siege well, they live long, but they die horribly and there is no coming back.
So I know what you're thinking, "get to the point". Ok here it is. Human are consistency so they almost exclusively are able to be revived. Lich are numerous and cheap so they die, resurrect, die again and potentially even redirect again. Dwarves are strong and expensive, so giving them revives would be borderline op, however if the lich can do it the dwarves can too. So my thought is to make them repairable. Whether it's a new menu or a new building to level all mechs would now be able to be repaired, for a price. So on my server I just started over on to alt dwarves my tier III silver mechs cost 17 mithril and 256 gold, one dies and I pay that same price if I want another. But if there were a chance (should be 50% or higher in my opinion based of race themes but hey, that just my opinion) for them to not die but rather be broken down then you would have to pay to fix them. So in theory it would only cost 8 mithril and 122 gold to fix that mech. So if I go in and lose 5 mechs (a full unit) and 3 are broken rather than dead I save resources making them slightly more powerful overall with tilting the balance of pvp.
These are my thoughts, sorry for rambling, I love opinions both similar or different from mine so let me have it.