Yes, absolutely, you should remove any crab before the mains touch; just think of the forces on the main gear otherwise - be a pilot, don't be lazy !
My technique is to flare and de-crab as one smooth coordinated movement, so crosswind flares are different to head/tail wind flares.
Myself and my then pilot colleagues came up the long way from flight school - via small turbo-prop twins, larger turbo prop twins, even larger turbo prop twins, medium sized four engined jets, then onto medium and large twin jets after about 3 years experience. So we had lots of landing practise on the line in all weathers, in aircraft with very little inertia and stability, so we perfected our crosswind technique before moving onto the big jets. Coming out of flight school straight onto a medium twin jet must be quite tricky in terms of manual handling !!
In my experience, SIMs are often wasted because we spend a lot of time in them flying around the hold working through long tech problems or doing Loft exercises. That sort of procedural practise could be done in a much cheaper fixed base SIM. The full SIMs should be taken advantage of for manual handling practise. No SIM can perfectly reproduce all the physical forces - because obviously they can't physically move very far - but a crosswind approach and pushing straight in the flare could be practised - leading straight into a go-around perhaps rather than touching down.