Whoops, that was a typo on my part - I meant to write 25 seconds in my example, where I compare these two:
45cm RG (4 shot) V80/C10 - 650 tons - Crew 39 - HTK 6 - Cost 554.3 - ROF 25
40cm RG (1 shot) V80/C10 - 178.75 tons - Crew 11 - HTK 1 - Cost 240 - ROF 5
At point-blank, the latter does 12 points of damage per hit whereas the former does 16 points of damage. So far so good, right? Well, you can have 3.64 of the single shot guns for one of the multi-shot guns. So even if you just have 3 guns it means you have room for more shield or armour or whatever, you'll do theoretically 12x3 versus 16x4, still okay. But then the ROF kicks in and this is where it breaks down because in 50 seconds of firing:
-the multi-shot 45cm RG can theoretically do 128 points of damage if each four shots hit both times the gun fires.
-the single shot 40cm RGs can pull off 360 points of damage if all three shots hit every 5 seconds.
And because the SS RGs are firing more often, missing a shot is less harmful whereas missed shots for the MS RG are far more detrimental. Only downside is increased MSP consumption but as said, using 3 SS RGs leaves you quite a bit of extra space.
Sure, the MS RG has more HTK and is slightly cheaper than the 3x SS RGs but that's a worthless advantage in comparison with the damage difference. This is why there really is no meaningful choice to make here: with large calibres, a SS RG is always better than a MS RG because you can get it down to ROF 5 and you can pack more of them in the same space. Only if you can get the MS RG down to ROF 10 (320 points which is still pretty far behind) or ROF 5 will it be competitive. But that requires big RP investment in capacitor tech and if tech parity exists, then your opponent can get bigger calibre SS RG's down into ROF 5 so they actually stay ahead.
It's really weird that you're using different calibers to illustrate the difference, since it's a specific example that makes the problem bigger. And then ignores things like power plants or the extra range of the larger railgun.
Let's try an example that uses the same size railgun and accounts for things like power plants:
4 shot 25cm Railgun V50/C3.75: 20 damage, ROF 20, 400 tons, HTK 4, Recharge Rate 3.75, Cost 72.6
1 shot 25cm Railgun V50/C3.75: 5 damage, ROF 5, 130 tons, HTK 1, Recharge Rate 3.75, Cost 36.3
Exact power plant tonnage varies based on the size/efficiency curve, but my standard powerplant in that game is 142.5 tons, produces 30.79 power, and costs 92.4. Adding that to the above numbers, we get:
4 shot 25cm Railgun V50/C3.75: 20 damage, ROF 20, 417.3 tons, HTK 4, Cost 83.9
1 shot 25cm Railgun V50/C3.75: 5 damage, ROF 5, 147.3 tons, HTK 1, Cost 47.6
By any measure except burst damage and point defense fire, that still greatly favors the single shot - it does about 2.8x as much DPS per ton and about 1.8x as much dps per cost (which is less of a factor, as the support systems on a warship often cost significantly more than the weapon itself), but I think your example considerably exaggerated it.
My complaint is more that simply giving them the same ROF just reverses it - the multishot maintains the advantage in burst fire and point defense but now does 1.3x as much dps per ton, meaning reduced shot railguns will basically never be used and it's otherwise a quite cool mechanic.