Joining the chorus here, shipyard repairs should absolutely be cheaper. Probably needs to be 1/3 or 1/4 the cost, certainly something less than the MSP cost to repair in-flight as otherwise the MSP repair is still broadly superior aside from micro-managing the mineral costs.

I would just make damage control not refill the ship's HTK.  If an engine gets blown up, and DC repairs it, it would function again, but your ship would still have lower HTK that wouldn't be refilled until you could get a proper shipyard repair.  Basically the duct tape and twine repairs are functional, but the ship's structure is still swiss cheese.

It would be neater to make shipyard cheaper. You don't need to make the whole engine from scratch, there's something left.

Shipyard repairs are twice as expensive (and usually take much longer) than field repairs using damage control.

My case: I have two damaged ships of the same type. Both have two engines destroyed. An engine costs 62.5 BP, all in Gallicite.

Repair in a yard costs, much as expected, 62.5 Gallicite per engine.
Repair via damage control costs 125 MSP per engine, twice the BP cost of the component in MSP. 250 MSP total. 1 MSP costs 0.25 wealth and 0.25 minerals; 0.1 Duranium, 0.1 Gallicite and 0.05 Uridium. 250 / 4 = 62.5 minerals, only 25 of that in Gallicite.

So if I repair the same two engines via damage control I pay half the minerals (and wealth), not to mention being done after a few days instead of a few months.
In my current game case I benefit doubly because I'm short on Gallicite, but care less about the other minerals: I only pay 20% of the engine's Gallicite cost by using damage control.

The example should be applicable to any component, not just engines. MSP repairs cost half as much and transmute the mineral cost into the generalized distribution that MSP production uses, which may or may not be advantageous depending on your gameplay situation (but I'm supposing here that it is usually advantageous as you pay less minerals overall). In my case (Gallicite shortage), it's advantageous to combine repair methods: Fix all engines with MSP, then repair the rest using yards to avoid spending any more Gallicite-costing MSP.

What do you think about this state of affairs? Am I missing something or not considering some case?

One one hand I like that Aurora's system allows (micro-intensive) optimization like this, but it seems backwards that field repairs are cheaper than professional ones. I think the proper solution would be to make field repairs somehow inferior to proper repairs (give only 80%of engine power output, lower tracking/damage/firerate, etc.), but that does not fit into current mechanics. Just doubling MSP cost of field repairs would at least make them cost as much as a proper repair, but still be faster and give the option of paying a generalized cost instead of the "proper" minerals a component is made of.

Some other notes:

Fuel storage has a cheaper cost noted than what they actually cost in minerals, that may make these components especially cheap to repair using MSP. Why don't they have mineral cost = wealth cost anyway? I thought they were made cheaper mineral-wise in C# already.

There is one downside: Field repairs may be impossible if a ship can't carry enough MSP to repair an expensive component. Since damaged ships can't be refit, just bolting on more maintenance storages isn't possible. Logically it'd make sense that some systems are just too big and complex to be fixed by the crew. Doubling repair MSP draw would increase this downside, too, preventing larger components like engines from being repaired in as many situations.