Bridgestone are the largest tyre producer in the world with motorcycle tyre plants at Nasu, Japan... where they make 30,000 tyres a day. The only other site making bike tyres makes low-volume ATV tyres and is part of an automobile tyre plant.
The GP tyres are hand-made at the Kodaira factory, near Tokyo
The workers that hand-make those GP tyres are very experienced, very specialised. You really are showing a deal of naiveté if you think that they can just up and make them at any plant. If that was the case, they would have done so back when they were competing with Michelin. It wasn't that they didn't want to, they just couldn't make overnight tyres and get them to the race... Michelin had a similar problem in Australia, USA, Japan, Malaysia - so for those rounds, they didn't - what they had was a specialist truck that could make a couple or four tyres specifically for Rossi and his team-mate and selected others, but due to the nature of GP tyres, it was a very limited run.
Michelin and Bridgestone have a very different ethos when it comes to racing tyres. Bridgestone make 'the best' carcass they can, then adjust the compound to give the characteristics the riders want. Michelin have set compounds and vary the carcass to give the characteristics the riders want. This allowed Michelin to have this on-site service. They didn't need to have a mini-factory, they had their (limited) range of compounds, the 'special' was all about the lay-up of the tyre. Bridgestone, to offer the same service would need a chemistry lab on wheels, with the necessary constituents to mix, mould, bake a tyre to a specific formula - which is why they needed to make them in Kodaira, not in the back of a truck.
A GP tyre isn't just stamped out like any other road tyre - it takes about 10 hours to make. It takes specialist hardware, moulds and chemistry. It takes special autoclaves to cure them and most of all, it takes a team of very, very specialised workers to do it.