I feel your points are valid but don't really express enough detail. The supreme court in the UK though named the same doesn't really hold anywhere near as much power for the following reasons:

1) There is no written constitution, the supreme court in the UK is only there to interpret existing laws as written not to interpret differences between "tiers" of law

2) The UK has a system that can pass new laws, generally by simple majority so any decision rendered about existing law can be made obsolete generally fairly quickly (In contrast to the current intransigence of the current US system where it is hard to pass primary legislation and virtually impossible to modify the constitution)

3) the court was only established in 2009, and evidently we haven't done much to empower it

A better comparison country might be places like Canada or Australia who do have a written (and harder to modify) constitution.