You might get a bit more with 25m vehicles but it won't be that significant, you also have the problem you now have a train containing 624 people with only two toilets. Good luck with that.
An Avelia Horizon
in a one class configuration will hold 740 people.
So that is a 15% reduction in capacity.
Wow, a double deck 200m high speed train has 119% of the seats that a single deck 200m high speed train can supply. Oh, and we're looking at innovative double-deck trains that soundly beat the 630 low-cost seats of a Ouigo Duplex by finding additional ways to cram people in!
9-car Class 80x trains fit 600-650 people with a generous proportion of first class: 510 standard +101 first seats (LNER) or 580+70 (GWR). But they are just over a car longer than 200m. There's 92 seats to a standard class car on GWR, with luggage space in each car, and 10 toilets (2 disabled ones at the ends, 8 others) on the train. 6*90 is 540. There's 60 (including 2 wheelchair bays) in the front end with a disabled loo, but you need a kitchen/crew area too - there's 13 first class seats, the staff/cooking area and a loo in the back end. Let's call it so the end carriages average 30 seats each on a fully standard class train. It's probably more, but it makes the maths easier.
Let's say 600 standard-class seats on a classic-compatible and 750 on a double-deck captive train. Is it worth all the problems you list below (stairs and the like) when you can get 80% of the seats on a single-deck classic-compatible train with the seating and facilities of trains running intercity services?
The staircase to the bottom deck takes up room on the bottom deck that can't have seats or standing room in it.
But you can't put a seat under the bottom few steps of the staircase from the bottom deck to the top deck on a bottom-deck loading service - it's a problem with any train with stairs that you will lose seat space to put in stairs.
Also it will kill your dwell times because everyone boarding the train has to immediately use a staircase.
But you want people to do that from low 760mm platforms onto trains that won't run entirely on HS2, or not serve Liverpool, Preston York, Sheffield, Stafford, Stoke, Scotland and Newcastle and render the scheme politically impossible and no good at doing what it was built to do on the WCML...
I agree steps kill dwell time (a problem with all bi-level trains) - but if you are only running 9tph each way through Old Oak Common due to only having captive trains, who cares as they won't block the train behind!
Plus, as an intercity service dwell times are going to be fairly long anyway, the steps issue is absorbed into that.
RER-A somehow (I still don't get how a high-frequency high-capacity line like that is able to run double deck trains at all due to the dwell time issue - perhaps it's overstated?) manages despite having the mezzanine boarding system. I therefore don't see why having a mezzanine is a deal killer on dwell times if double-deckers in general aren't.
And how will step free access work on this service?
Will people who struggle with stairs be required to sit in the vestibule?
Lifts, same as they would have to have on bi-level trains with bottom boarding to go up to the top deck.
We should do everything possible to avoid single deck trains.
Why? You've just strongly made the case that double-deck trains are not very good: an underwhelming capacity boost from the second level coupled with dwell time and accessibility issues from having two levels.
Most places where the train goes less than hour out of London have 3+2 seating, why don't we do that here too?
Its would cut ticket prices by 20%.
So 3+2 adds as much capacity as double-decking - 5 seats for every 4? Tell me why we need to avoid capacity-reducing single-deck trains again? We can surely just have outer suburban seating layouts rather than intercity layouts and get the same number of seats in as having two-floors?
I think, however, that doubling the number of seats by running 400m trains instead of ~200m trains to Birmingham is going to be enough extra capacity to be getting on with for the time being. It's worth considering captive sets for when phase 2b is built - we wouldn't be looking at a small fleet of 9 or 10 trains then (and the classic-compatibles can cascade from Birmingham and Manchester routes to serve Sheffield and Newcastle). These captive trains could all have high-capacity 3+2 to make things easier - Manchester's only 67 minutes (same as Marylebone-Aylesbury Vale Parkway with 165s), Leeds 81 minutes (less than Liverpool St-Clacton with 321s).
Clearly we ought to go with awkward middle seats rather than mucking about with awkward stairs to get the bonus capacity boost, when we go with captive trains. That is, if we want that additional bit of capacity on top of that already added, rather than use the captive trains' larger size to provide more comfort instead.