You already named two arguments (acting on different theatres, power splitting) and my additions are more refinements of both: You can have some spezialized fleets (main combat, pirate control, transport, slave raiding, siege) and having more Admirals can help you with job managment and great families (though the extra wage cost is to consider). In Republics, it is also important to keep in mind that Admirals weight in 100% of their powerbase in the senate (not realistic, but was deemed necessary by the devs to avoid a stronger exploit - and so that minor one is allowed to make use of this for manipulating faction powers in the assembly).
But on the whole, I lean towrds your statement - go with one navy, unless you have one or more clear reason(s) to split. Splitting was crucial, when the reinforcement bug was plagueing any larger sea fight, but it is luckily gone. I personally tend to split fleets, but I do it more for roleplay reasons and employing characters with Admiral traits with appropiate jobs.