I believe the thinking here is wrongheaded.
Primitive mechs exist either in deep periphery areas that never had the level 1 technology, and as historical units.
Just because something is primitive doesn't make it cheaper. It might have lower BV but that doesn't mean anything to a procurement department.
A planet wanting to make a mech factory must tax the same number of goat farmers the same number of goats to get either technology, primitive just being easier to come by.
Lets take our own history, a first rate battle tank costs about as much to build in real terms if it is a Panther, a Conqueror or an Abrams, you can either build better or you can't, and that is due to access to tooling and technical know how, and in some cases materials, not money.
If you want to go primitive you need to learn from the Capellans, who remembered history and came up with the Po, or for that matter the Vindicator, but the latter was in somewhat better times. Both were rugged and reliable and held to the accessible technology of the time, but never left common sense behind or became too cheap to be of good service.
If you want a budget mech for lean times take standard technology and build it cheap. Make it light but don't pile on the speed, engines and gyros are expensive. The classic AC5 and medium laser is a good baseline for firepower, but with 4/6 rather than 6/9 speed on a 40-45 ton chassis. Armour is cheap too, so you can afford max out, and skimp on wunderfwaffe like the PPC. Then double down and make zillions of the little bastards, fill them with half trained conscripts, distribute them to all your border worlds and throw them at the enemy.
My favourite concept for a backstop mech design, yes this is head-canon but we are speculating; was to take a very generic mech: Stinger or Wasp. Take your pick it won't matter and retrofit it with a three or four ton chassis. Build accordingly, but keep all the advanced equipment just as it is. Which means cockpit controls, myomer, engine and gyro being direct port overs. The only energy weapon allowed being the ported over medium laser, so you are adding light autocannon and missile racks only. A 30 ton Stinger becomes an honourary medium, with some limited firepower, with I think the better choice is a 40 ton Stinger which becomes a 'micro Atlas', same 3/5 speed with room for a small autocannon and some missiles. It probably doesn't jump because they would involve a lot of recalibration which goes beyond the scope of the design studio. I suspect it wobbles a bit while moving at run speed. But it should have dangerous firepower, especially in numbers, enough armour that they would be a chore to shoot through and are likely available in obscenely high numbers distributed over a lot of backwater planets.