I mostly play with small fleet sizes where this issue virtually [edit:
never] crops up but have recently started a Germany game with super-large fleet and yeah, I can see the "problem".
If you want to role-play, I think the country you play would play a role in this too.
The UK in the time leading up to WW1 was easily capable of building 6+ capital ships at the same time, Germany was a bit more limited (4 or so sounds like a reasonable number). Austria-Hungary would be even more limited, I'd guess.
If I'd implement such a house-rule, I'd group the nations like this
UK: Up to 8 capital ships and a virtually unlimited number of lighter units
USA: Up to 6 capital ships and some 20 lighter units until the mid 30s, then like UK
France + Germany: Up to 4 capital ships and around 15 smaller units
Japan: Up to 3 capital ships and 10 lighter units until the mid 30s, then like France/Germany
China, A-H, Spain: Up to 2 capital ships and 10 light units up to the late 20s early 30s, then like Japan.
Of course, this is all looking at it a bit through historical glasses, while we are creating an alternate history, so you could also base this whole thing on the number of ships build prior.
Like: Build (or have the game build) your legacy fleet.
For every 3/5/10 (whatever number floats your boat) ship in a specific class you have in your fleet, you can build 1 ship at a time
For every _additional_ (enter chosen number) ships in that class, up the number you can build at any one time by 1.
Example: You chose 5 as the number.
Your legacy fleet starts out with 9 B, 8 CA, 7 CL and 25 DD
You can build 1 B (9/5 = 1.8), 1 CA, 1 CL and 5 DDs at any one time.
After building 1 more B, you can now build 2 B at a time, since your nation has now build a total of 10 B.
If you want to build more than a single CL at a time, you would have to build 3 new CL to get the number of CLs you ever build also to 10
Or go with a combination. Start with a number you set for yourself (either for capital ships or for each ship-class separately) and then increase that number per so-and-so many additional ships you build.
It would involve quite a bit of book-keeping, though.
Of course, there is the little problem of the AI, that is in no way, shape or form restricted in a similar way.
In my aforementioned Germany game, I'm outnumbered in B by the UK about 2:1 while building B and CA as fast as I can - limiting myself to only being able to build 2 or 3 B at a time?
Yeah, there's no way that will end in disaster at all
In addition, if your budget is large (like in those very_large/super_large fleet games), you will repeatedly get the "you don't need all that money we gave to you, so we take it away and cut your budget to boot" event from your government, because you're sitting on a gigantic pile of cash you can't spend - since you can't build more ships.
Now, you may say: Hey, that's realistic, if a navy couldn't build more ships, they couldn't spend the money they had and the government would reduce their budget and that'd be correct but to my knowledge, that was something that almost never happened. It was always* the other way around. The capacity to build more ships was there, what was lacking was the funding for it.
* Yes, Germany, pre WW1 couldn't have build a similar number of dreadnoughts as the British, simply because their ship-building industry didn't have the capacity - but the Imperial Navy didn't have the money to do that anyway.
So, in conclusion, my feeling is that having the budget as the limiting factor seems to me to be quite correct, historically, except for very few exceptions and that is where dockyard size comes in (I'm looking at you, Chin China)