I think we established that Cali can ill afford doing a Perry?
And what does it gain them? A war they can't win, or a conflict so long and costly they might as well accept that embargo and not interact with anyone but those few states that would trade with them.
What are they going to do about damaged ships in case of a conflict? They can't call in a transport ship, or even a tug. They have no ports that can accept their warships due to sheer size.
A super carrier could
run over your average warship in the 1950s and not be damaged. Not that Britain would ever get close enough to be run over. Also, there are a number of ports that can accomodate all the forces California would need, especially since among the assets in California are groups with experience in preparing landing points.
However, If Britain say, decided to push things? You wouldn't even need a supercarrier, or LHA, or really much of anything beyond a very small force.
Said force to be:
1. A small support ship, a modified cargo ship with a flight deck, some 35mm cannon and a modified Hellfire launcher, which means it can comfortably kill anything on the seas long before coming into range.
2. Aboard said ship, four Apaches. Each apache can carry 16 hellfire missiles--which means that
each apache can mission kill or outright sink
sixteen british warships. They can do this in the middle of the night, when the British can't even see them. If you don't want to pay the cost of the Hellfires, that 30mm cannon will do the same job with a little more time.
So sure, fielding a supercarrier might stretch logistics a bit. good thing in a fight, California can destroy the British fleet around their isles and completely destroy Britain's ability to project power without ever needing to sail one out of San Diego harbor..
Meanwhile, a small amount of that single ships cargo bay, say 500 tons or so, will be used to provide the
Irish with more than enough firepower to destroy the British colonies in Ireland, especially since any attempt to supply them ends in death-by-hellfire.
Don't forget, there is not a
single nation in 1850 that doesn't have enemies, or doesn't have internal groups that would be very eager to secure their freedom. California doesn't need to deploy divisions of tanks--a few humvees with grenade launchers and towed 81mm mortars is going to utterly smash any downtime force you care to name, especially if they're working with local support.
The great powers of 1850
know this. They know it because they played the same game with many of their current colonies and were able to do so when the technological field is
vastly more equal. They're not going to be even thinking of trying to play hardball with the most powerful nation in human history.
In a fight, California isn't so much a regular military, as they are George Pal's Martians--only without the whole "flu" issue.