The answer is for XC to run trains of the length they should be running them and this would negate whether there is a need to de-classify first class in these situations.
Now that XC are only running one train an hour on Manchester - Birmingham/South Coast and West Country - North East routes instead of the normal half hourly service on each (with four or five car trains), then there is no reason (excuse) for these trains not to be running in double formation. That way, although there is the inconvenience of loss of frequency and through service, at least the doubling up compensates to an extent for this. However, I notice that this doubling up is not happening as and when it should be, at least on the Birmingham to Manchester on Sundays. Clearly, from what others have posted, this is also happening on the West Country - North East route as well.
Sunday is one of the busiest days on XC routes but I noticed that quite a few services on this route are formed of only four or five cars. Sometimes, when there is a double unit in use, one of them is locked out of use. All in all, this low frequency/short trains/ trains locked out of use etc results in some quite horrendous overcrowding, passengers crammed into vestibules etc, and is totally avoidable and unnecessary. XC are blatantly taking advantage of the situation to reduce their costs/boost profits, which they wouldn't be able to do if they were still obligated to run the half hourly service of 2 x 4/5 cars. I am not talking end of day lightly used services here. This is happening on busy Sunday afternoon and into the early and mid evening services and happens every Sunday, so it's not as if it hasn't been foreseen and XC are not aware of it.
BTW - XC are not the only operator to exploit the running double units to compensate for reduced frequency principle. LNWR also run the Birmingham - Liverpool service as four car only on a Sunday instead the eight car that it is in the week. which results in similar overcrowding on that route. It does mean that passengers travelling north of Birmingham to either Manchester or Liverpool are being doubly cheated and 'mugged off', as the reduction in frequency is not being offset by the use of longer trains on either service. The same is clearly happening south of Birmingham on the XC Manchester originating trains that continue to Reading/Southampton/Bournemouth.
DB (German Railways), that run XC, would never treat, or get away with, doing this in Germany, where long distance trains linking key regional centres are run with full length 'proper' Intercity trains. The same applies with Abellio (Dutch Railways), who run LNWR Birmingham - Liverpool trains.
XC clearly don't care and I guess the Government don't either as they are footing the bill right now.