So increased randomness of the deck due to the higher card amount and increased scarcity of the resources cards set aside, is there any other issue that could brake the game if I increase the number of allowed cards per detachment?
Depends on the faction/detachments.
Some 'strategies' are only really present in the base game, and straight up adding cards might dilute them to near worthlessness.
Cryx has a few good quick examples:
Cryx Orange is mostly 'Stitchers & Stitched'. One of the expansions adds 5 Stitched minions (2 Orange, 3 Yellow) with notably 0 Power, but no additional 'Stitchers' with which to power boost them.
Likewise Red/Yellow has a 'Scrap' theme, which is not supported in any of the expansions.
And none of the expansions support Combo Strike (Orange/Blue).
Meanwhle Cryx Green doesn't much care what you do, as there isn't much synergy between its cards to begin with.