Points 1) and 3) would rule me out. I won't climb gates and I like to keep the option to work Saturday during busy periods. Also, I don't do monthly so they would need to agree six weekly. That's not arrogance, that's business sense. I'm not going miles out of my way for one house when everyone else is on a different rota from them.
However, neither point is insurmountable. I don't like texting ahead for access, but if they were prepared to leave it unlocked, it could be a runner.
What I will say though is that potentially, I would lose the occasional clean when they are on holiday and there is the potential to occasionally disrupt my schedule due to 'no Saturdays'. Therefore, the service would come at a higher price.