So I call NHS Direct, they agree that unexpected blood is potentially urgent and I arrange a taxi in the middle of the night to go to the closest Urgent Care clinic. Taxi driver did completely fail to find the right entrance to the hospital, but I was just sick not stupid so I followed the signs he'd ignored and went to Urgent Care. I was the only adult, every other patient was a sick child whose parents were probably worrying too much. A doctor takes a look, goes yup, just what you'd expect, not serious but thanks for checking, disapproves of my "Crisps and full fat Coke = Salt + Sugar + Water = acceptable rehydration" approach and hands me nasty tasting rehydration powder. Boo but since I'm the one who just dyed a toilet bowl red with their own blood I vow to follow their instructions. Taxi back to the hotel. All better in time for the trip home. Still have the last sachet of rehydration powder somewhere actually, it's probably expired but can't taste worse now than it did then.
NHS Direct is really handy, because it's often tricky to judge the correct amount of urgency or know how best to access the service you need, especially when far from home. But I don't see how you could build a trustworthy service like that under the US system.
I know in other countries ambulances are not always dispatched, because 911 operators decide it's not critical.
Mostly this decision is correct, but from time to time a heart patient dies. (Maybe the alternative should be to send a taxi)
But I don't think the dispatch taxis instead -- besides our taxi availability is highly limited and extremely expensive (Uber being prohibited). To be fair taxi drivers are certified, and service is IMO high quality.
On the other hand, given that triage failures are rare -- cost/benfit wise it's probably better.