Squadron splitting

As far as I know splitting squadrons does not cost anything: if there was no battle action yet, I can just announce that from that point on I split a squadron and assign a new flagship to the newly formed squadron (Please correct me if I'm wrong).

The problem we are having is that can lead to gamey tactics in some scenarios. For example, in "Buying time" scenario it says the attacker can place 1 squadron on the board at the beginning of the game. What if a player puts all his (core) fleet in one single squadron? Then he can put all his ships on the board before the game starts and split them in the first turn. This gives him a big advantage and does not rely on luck to add all his ships to the battle in later turns.

Have anyone encountered this problem? Or am I maybe missing/misunderstanding a rule?

Yes you are correct on both counts, this is something I'm struggling with a bit. In lieu of the same issue, I noticed that often I forget to mark flagships completely and only discover late in the game. The feature seems to have outlived its purpose a bit but I don't really know how to solve it elegantly.

I have encountered this in game play. I feel there are a couple of ways to "fix" this. One is to ignore it and acknowledge the fact that some players may take advantage of the rules as written. When I did historical fleet line ups for some of my pacific battles, especially the carrier actions with the rules as they stood, you could have a couple of carrier squadrons with a determined number of escorts and then one escort group. This escort group was always pretty big and usually split and added to reinforce the carrier groups or just split into extra groups. I have also played games with more squadrons than the leader can "control", and only order tokens up to his max are generated, the other squadrons tokens are "lost". Though again this does mean that the degradation of orders takes longer.
A way around this is careful scenario planning. X ship/squadron cannot start on table, or only certain ships can start on table? When designing many of my games I just decided which ships when.... With the scenario parameters in the rules as guides.
A thought would be that you could add a specific time in the turn to allow for regrouping. So either before orders are generated each players determines the make up of his squadrons, doesn't have to declare which are flagships mind. Or this is done in the end phase? Another alternative would be to only allow a squadron to voluntarily change composition on a movement activation?