Because the framework is already done - they’re just having a standoff now about the payment schedule.
Arsenal won’t be bothered at the moment as Rice will still be on holiday like half the City squad, and even if he missed a week, he’s an England international with 100+ PL appearances, it won’t harm their season.
And honestly even if they walked away, it wouldn’t be any more ‘tinpot’ than City were walking away from say Sanchez or Van Dijk when the deal became dumb to do, it would just look silly on West Ham if they had to sell him to Chelsea for example for less than Arsenal offered.