Not a huge fan of 222's but they would certainly be better suited to a service like Liverpool-Norwich.
I would also like to see the following stopping pattern on that route;
Liverpool Lime Street - Warrington Central - Manchester Piccadilly - Stockport - Sheffield - Chesterfield - Nottingham - Grantham - Peterborough - Ely - Thetford - Norwich
Does it really need to call at Liverpool South Parkway and Widnes, when there are other local trains that call there? Maybe TPE could stop there instead.
Also, Alfreton. Not really sure this justifies more than 1tph to both Nottingham and Sheffield.
It could also speed up journey times on this line.
Widnes is quite a large town. The stop there provides a fast service between Widnes & Manchester, and you would probably lose many of these if they only had local services, many operated by Pacers.
Liverpool South Parkway is attracting passengers who use Liverpool (John Lennon) Airport.
After electrification of the Chat Moss route & the Trans Pennine lines, there will be no TPE services via Widnes.
I think 4 car 158s between Liverpool & Nottingham are adequate - although unfortunately some 2 car trains still appear. However, it would be useful if there was also an hourly Liverpool - Manchester - Sheffield - Derby - Leicester service, also 4 car 158s, to increase capacity over the busiest part of the route. (But please - no first class - that would only leave more standard class passengers with nowhere to sit.)
(5 car 222s have a lot fewer standard class seats than a 4 car 158, so we don't need 222s to "improve" the services; even 7 car 222s have only a few more seats than 4 x 158. )