Yes, the Sunday start for weekly capping is very inflexible. Also, if you use contactless ‘too much’, you have to use your PIN every so often. No problem in Tesco, but, if it happens at an underground station, you get a declined transaction, no help from the staff, and no weekly cap. So, I use Oyster for all journeys.
You won't get asked for a PIN validation when using contactless for transport as there's a separate 'transit mode' than contactless cards use