There are a couple of dangers here:
If we return to the old system where one can pass directly the Class 1, and then acquire the entitlement to drive class 2 and wagon+drag entitlements despite having had no training/experience at that point:
WHO will, in future - choose to do the now optional Class 2, just to get lumbered with the huge amount of “Knowhow”-type work available, rather than “Dead Man’s Shoes” Bakery jobs?
This government decision - could very well merely shunt the current overall HGV worker shortage - to a C2 shortage, which then in turn - leads to the rising of C2 wages up and beyond what C+E drivers get…
The other danger is that should C2 pay rise in this way - that C+E holders, especially the younger, fitter ones among our number (!) will opt to ditch their C+E job for a now-higher-paid C2 job, leaving the “shortage” to then run full circle.
The major factor that the government seems to be side-stepping at present - is that their solution sounds like a long-term one, but in fact would only work if we returned to pre-lockdown levels on pretty much everything - soon.
I think that we’ve entered a new era, like it or not though.
Nothing will quite be the same again, and the next economic boom - will only be for those workers who’ve decided not to return to their former lands across the seas… 
“Rustics you were, and Rustics - you are still.”
(The Peasant’s revolt - rose up following a severe labour shortage among the decimated population following the Black Death two generations earlier…
A possible sharp rise in pay and conditions, due under the basic supply-and-demand capitalist system - never happened thanks to the actions of young Richard II, who was later overthrown and left to perish in a dungeon by future lancastrian usurper - Henry Bollingbrooke, aka Henry IV of England…)
To this day, “Supply and Demand” only seems to be one-sided, and entitle already-wealthy employers to get rid of people when there is a surplus of labour, and not upkeep the common good when “Times are 'ard”.
In my mind, it is those who have prosperered under the lockdown - that should bear upon their shoulders the full cost of any future recovery.
There’s no point even attempting to kick people at the bottom from here on, as a lot of us are dropping out of tax, due to low earnings. You can raise basic income taxes as much as you want then, and the Rich will offset ever more, whilst the poor don’t earn enough to pay those raise taxes.
Clearly, a different solution is required.
The Government’s current direction on post-pandemic Britian - will likely fail the moment future foreign settlers here - rely on the state benefits, rather than strive to get one of the now MANY low-paid jobs in our economy.
Meanwhile, home-grown Brits - are not going to be choosing to come off benefits or even Furlough - if their new job and duties has them working twice as hard, half as many more hours, for only 20% higher pay than before.
Inflation - will likely erode away the 20% pay rise as well, with Gas up 800% from the lows of last year alone…
At least there is growing pressure to keep the “Temporary” uplift in place, due to otherwise end at the “End of the Lockdown”…
(Article 2 hours old at time of posting this edit.)