I'm not sure how not building the HS line to Crewe will result in Liverpool trains being faster to London than keeping tilting trains between Crewe and Liverpool.
As the journey time's are as follows:
Avanti class 390 (passes through Crewe and one stop at Runcorn) 35 minutes.
Avanti class 8xx (calls at Crewe and two stops, one at Liverpool South Parkway and the other way Runcorn) 40 minutes.
West Midlands Trains class 350 (calls at Crewe and three stops; Mossley Hill, Liverpool South Parkway & Runcorn) 40 minutes.
Assuming zero penalty for the stops, the best you're going to achieve is 5 minutes.
Under phase 1 journey times London Crewe would be 68 minutes, with 2a that was due to reduce to 55 minutes, by my maths that's 13 minutes of savings.
Therefore, unless we want to disadvantage Liverpool any alternative scheme to 2a would need to find journey time savings of at least 8 minutes, quite probably 10 or even 11 minutes due to station stops having a time penalty.
Also, by using tilting trains with a lower top speed compared to non tilting HS2 trains, it's likely that a further few minutes of time would also be needed to be made up by the alternative proposal due to the extra journey time between London and the end of the HS infrastructure.
However, phase 2a appears to have also been able to deliver 10 minute savings between London and Manchester (phase one journey time saving of 30 minutes, phase 2a the saving increases to 40 minutes and the full way to Manchester the saving increases to circa 55 minutes). As such, there's wider benefits (before we consider any congestion and local service benefits from removing the faster trains from the existing rail infrastructure) which could mean that the value of building phase 2a is better than building a cheaper option.
Now sometimes a slower journey time of (say) 10 minutes isn't going to alter the attractiveness of a train, however that's often if we're taking about the choice between two routes.
For example if London Edinburgh had a 10 minutes difference between using HS2/WCML vs using ECML chances are the split in passengers using one or the other would be fairly much equal if there were no other variables, as whilst spending 10 minutes more travelling is a down side, depending on timetables that slower train could still allow a passenger to leave later and arrive earlier than using the faster train (especially on timetable frequencies where there's more than 20 minutes between those faster trains)
However, not building phase 2a and using tilting trains instead isn't a choice between two routing options, and so that 10 minute delay will result in a worse service for Liverpool than could be the choice if phase 2a was built.
Therefore, I find it odd that those who complain about Manchester getting a better deal from HS2 than Liverpool (even though HS2 wasn't proposing more services to Manchester, but a doubling of services to Liverpool and arguably that suggestion is the reason why Liverpool has seen the new Avanti services) would also suggest that not building phase 2a is a good idea for Liverpool.
Happy for someone to explain to me why Liverpool would benefit from slower trains or explain how the alternative doesn't result in Liverpool having slower trains.