But it is a Tier4 heavy tank that comes a lot later than a PZIV and especially way later than a StuG III G, which is a way bigger thread for it. Actually KW-1 comes halfway between PZIV and Panther.
It was good as it is as it was a call-In. In that days you skipped T4 and used the call-in to put the tech cost directly into the tank. That way the first KW-1 was pretty cheap. After putting the unit in tech it just got a bad timing space in T4. Ostheer PZIV and T34/76 both come out 55 fuel earlier, both have greater shock value for opponents infantry and are a lot more flexible.
So again. A buff of the MGs to T34/76 level is surely not too much to ask for. Some utility ability like a smoke shell or a infantry suppression ability would help to use it as a breakthrough or defensive tool (choose your liking).
I do have the feeling that it is a tiny bit underwhelming, but that does not mean that it would be uneconomic against mediums. It's bad against heavier armor where it can't really deal damage. And it can't really kill mediums unless your enemy is asleep due to relatively low speed (The only Axis tanks that are slower than the KV1 are also stronger) and low pen. KV1 vs P4 will just lead to an endless battle of two tanks slugging it out while bouncing at least half of the hits. This means that a big investment of the SOV player is not suited to really deal killing blows, since everything can retreat away from it, even infantry. So now it's in a weird spot. It's role is driving up and soaking damage, but the enemy is probably better off just focussing all other units except the KV1. A Churchill can deal decent damage on it's own if it's too close due to an okay-ish gun, MGs and hand grenades. KV1 is a bit worse in all categories, so ignoring it as long as needed is probably the better choice.
To your timing point:
Does it really come that much later (please correct me if I'm way off in the fuel costs below)?
OKW:
15 truck, 35 med base, 15 truck, 120 Panzer HQ, 140 P4
=325 fuel (likely +15 fuel for medics)
SOV:
15 T1, 85 T3, 80 T4, 145 KV1
=325 fuel
I think I'm somewhere off in the building costs, but not by far (maybe 10 fuel or so). SOV T2 build will come around 25 fuel later with side tech. OKW T2 build is the same 340 fuel.
Can't say much about OST since I really can't remember the building costs. I just know that BP1 is 40 fuel and BP2 is 90. Buildings were relatively cheap with around 20(?) fuel each, so 60 for the buildings, 130 for BPs, 120 for the tank would be approx. 310 fuel.