Yes, there was actually very little street running.
Whilst Merseytram had some weird details to it, such as the insistence of going to Kirkby via Tue Brook, the fundamental principle of serving the busy West Derby Rd corridor with something better than buses was a sound one.
I commuted from West Derby back in the day. It used to take about an hour, door to door; for a journey of under 4 miles.
The insistence on going to Kirkby was to ensure the involvement of Knowsley rather than it being just Liverpool. Even so, it didn't stop the other boroughs from giving it only the most lukewarm support. That was a fundamental problem with how the PTEs were set up before the role of Metro Mayor came along. It's what designed it and also what killed it.
If we did such things properly in this country, you'd run the tram along the 18 route enabling those bus services to be removed. Not serving Muirhead Avenue East and the Croxteth Park estate would've left these areas relying on the bus services which, considering they're deregulated, would been somewhat less viable by the tram abstracting its potential fares on the inner two thirds of its route.