Not if you use strict enforcement. Plenty of cities across the world manage fine, it's only the UK and US that cowers in fear of the car lobby.
When a tramway runs in a suburban street it almost always gets it own lanes. France has its "site propre", Netherlands has "trambaan", Germany has Trambahn. This is what I'm referring to by segregated running, not necessarily off-street. That's what would be difficult to provide in much of Cambridge.
In city centres it can run on street but general traffic is usually highly restricted. Slow running is less critical here because most people are starting/finishing their journeys and it's still quicker than walking. In places such as Oldham the design made sure to provide off-street delivery bays, but in central Cambridge the streets are so narrow that's unlikely to be possible.
As stated, the video shows this isn't the case. If you have the space and budget for a segregated right of way then yes, do that. But if you don't, it isn't the show-stopper that you're presenting it as.
I don't need to view the video - I was on the design team for Phase 3 including Ashton and Oldham.
Quick measurements off mapping:
Ashton terminus to Audenshaw - fully segregated except road crossings - 2.9km.
Audenshaw to Droylsden - segregated lane one way - 0.9km
Droylsden to Clayton Hall - with traffic - 2.4km
Clayton Hall to Holt Town - fully segregated except road crossings - 2.5km
Merrill Street - with traffic - 0.2km
Pollard Street to Sheffield Street - fully segregated except road crossings- 0.9m
So the part running with traffic in both directions is only about one third. Perhaps that appears to be longer on the video because it's so much slower?
The street running section in Eccles is about 3km. There's 4.5km of full segregation from there in to Deansgate-Castlefield, plus some at the Eccles end. The city centre is fully segregated from general traffic apart from junctions.