So it sounds to me like, in your game, Alert basically does give the character a supernatural warning when someone is planning to attack them? Which is certainly a legitimate way to read it. But if I were playing an assassin in such a game, I would try to neutralize it by hiring a bunch of people to plan on attacking the target as often as possible, without carrying through. Eventually I'd expect the target to stop paying attention.
For a non-supernatural example in fiction, try Captain America. He doesn't have super-senses or any superpowers; everything he does is within human possibility.
And yet....whatever happens, he's ready for it. He didn't know it was going to happen, but he's never caught flat-footed (to use a phrase advisedly). That's what being immune to surprised entails; it doesn't mean that you can't be astonished by a turn of events, nor does it mean you automatically succeed on every Perception/Insight check.
It just means that, whatever happens, you can use Reactions before your first turn, and can move and act normally on your first turn.
As for making plans to deal with an enemy's immunity to surprise (if they somehow find out about it), fair enough! Foe's will evolve their tactics.
Also, sensible creatures would adapt their behaviour to their own abilities. If I obtained immunity to surprise, I'd keep it quiet, try to disguise the fact. If I got that 'bad feeling', I might take an action that doesn't make it obvious that I'm not surprised: cast a Subtle spell, take the Dodge action (which means I'm ready to move out of the way, not that I'm cart-wheeling about the place!), pretend I need to urinate and go behind a boulder, even Ready an action for when/if an enemy does 'X'.
Even without the current surprise/immunity subject coming up, the DM can always start a combat, deliberately prompting players to waste spell slots and resources, having the baddies run away. Repeatedly. Annoyingly.
It will certainly have an effect, not only on the PCs, not only on the players (who start to get miffed), but also on the DM when
he is forced to swallow his own DM's screen the PCs start to do it to the monsters.