Or have some table API to control the tabs/rows/cells.

Using a programmable table with the option 'Also show tabs so user can pick row', you can do this very easily.
E.g. If your table has a name 'Table' and row/tab 1 is named 'A', and row/tab 2 is named 'B', then, just adding a cfd field $Table with a value of "B" will show the secon tab upon opening.
I use this frequently even with profile variables, to allow a user to choose wich is the preferred 'opening' tab. You can even use this technique to 'store' the last used tab.
So I demote, as this solution is way more flexible then setting a default tab in designer.

The programmable table option works, but unfortunately it seems to be persistent. If I remember right, an F9 shoves the table back to the opening tab. It takes making the programmed field @Unavailable before everything settles down.

So it works, but it's kind of hard to use.

I think it needs some heavy documentation on how to make this happen in a supportable way across multiple versions and deliveries. Either that or there should be some way to do the programming more nicely.