I have nothing against wood-look tiles. I would even prefer them because I think the look allows for more "character." I need tiles in terms of material because otherwise, the animals and children here would put too much strain on an affordable parquet floor, and I fear that the efficiency of the underfloor heating would suffer. I will not choose wood look because I am yielding to my wife's taste here. Somehow she has to be involved if I’m paying for everything and doing the work myself; otherwise, it won’t be our house.
I also claim that good parquet is on the one hand more expensive than tiles but on the other hand would definitely be available at the price quoted here (even solid wood planks). I believe your general contractor or the tiler is trying to squeeze something out of you with, in my view, questionable arguments. However, it is unrealistic to expect that they will lower the price again. It is simply a seller’s market right now. If I were you, I would either settle for other tiles from the selection or remove the trade entirely. But through my experiences with my general contractors (windows, staircase, doors, probably heating & plumbing), I have become numb to removing trades. In fact, I still cannot say if that is really a good idea since the in-house trades have not yet taken place. There is a risk of scheduling difficulties and therefore delays, as well as problems with warranty issues at interfaces (“The screeder did it wrong” – “No, your tiler!”...) that are possible! Whether it really saves money is something you first have to research... So it’s worth thinking carefully whether to take this step.