That is an absurd way to look at it, and I'm not just talking about spurious numbers. And the odd thing is that you've explained why yourself:Ca. 3% of the moves are tesuji.
A plain, ordinary door can be a useful thing. But it's actually quite complex. It needs plain, ordinary door jambs. It needs a plain, ordinary lintel. It needs plain, ordinary hinges, or a plain, ordinary sliding unit. It needs a plain, ordinary plain, ordinary handle and a plain, ordinary keyhole with a plain, ordinary lock. And, above all, it needs a fancy, extraordinary key. And often, the fancier and the more extraordinary the better.What one first needs is plain ordinary moves.
A tesuji is a move that fits in with the flow of the stones (碁の筋にかなった手). It is the 'key' that fits the 'door' made by the other stones. If you don't have a door, you are just a man wandering around aimlessly looking for a door to put your key in. If you have a door but no key, your door's not really going to serve the purpose you had in mind for it.
The key does not have to be too fancy - just fancy enough to foil most attempts to get through the door. In a go game, if someone flashes a really fancy tesuji 'key', there's likely to be mention of it in a commentary. But it doesn't mean there are no tesujis among the unmentioned moves.
In a hanetsugi, the last connecting move is often a fancy tesuji move that may or may not be mentioned, depending on the level of player the commentary is intended for.
On the basis of these 'unmentionables' I'd say the appeareance of tesujis in a real game is rather higher than 3%. But even if we stick with 3%, we have to include all the door stones properly placed in order to make the key work. Let's pluck another spurious figure out of the air. Let's say a four-move hanetsugi represents the basic minimum for a 'door' situation. Clearly, most situations involve more stones, but let's be modest and say around six on average. I've run out of fingers and toes, but I think that means about 20% of all moves, at a minimum, count as part of tesuji situations. If we strip out fuseki moves and trivial endgame moves or connections and the like, they form an even bigger part of the game. Maybe even the majority of the game, at pro level.
That's why tesujis are important. Go is a team game. All the stones have to work together. You are the manager that makes the whole team play well. If you're just there 3% of the time, you end up in the Fourth Division.
and 
reversed) White removes an eye but Black can continue with e.