How is it metagaming if the PCs in the setting know intuitively when they become capable of training - they've analagously in effect passed this round of field testing and are good for another bout of classroom instruction.
Great, they are ready for the classroom...
So what?
If the adventure is time-sensitive then they go back and finish before going to the classroom. At which point other PCs can likely join them.
If the adventure is not time-sensitive then they go to the classroom and the others can relax or whatever while they wait. In which case they return to the adventure with some stronger PCs.
As an example, look at what is happening:
A-B can train to gain level 2
C-E are all still level 1
F-G are possible new PCs at level 1
You go back with 5 PCs at level 1, even though 2 can't earn more XP
OR
You go back while they train with 5 PCs (adding F-G) that are all
still level 1
Either way, if you continue the adventure immediately, you have 5 PCs at level 1, but in the first case you are playing the same PCs because those are the ones you are playing for the game. In the second case, you are forced to bring in two new PCs to fill in the gap just so A-B can train. Now, you are starting your merry-go-round of PCs and juggling act of who can go on which adventure when because so-and-so needs to train but others want adventure and XP.
OR if the adventure can wait, A-B train and you return with 5 PCs but now 2 of them are level 2 and can earn XP as well.
There is no need to bring in more PCs
just because some need to train. Bringing in a new PC because it is something the player wants to play is a different matter, of course. Adding PCs because you are adding new players (what happens in the scenario in the DMG) is also a different issue.
Because those characters are not always there - they come and go.
Sure, it can happen for story reasons or player interest, but it isn't because you need them while others train...
The issue with carrying on untrained - and on this I'm nowhere near as harsh as original 1e was* - is that you start hitting a point of diminishing returns, where your earned xp suffer a penalty based on how far into the new level you've got.
* - in original 1e after bumping you couldn't gain even a single xp until you trained up, no matter what you did.
It's only an issue if your goal in the game is to gain XP. If your goal is to play the adventure, it isn't an issue.
Also, XP is awarded when you return from the adventure. The DM is not meant to calculate XP and award it on-the-fly, but at the end, when they can look at all the creatures defeated, tally the treasure recovered, etc. and adjust it against the difficulty of the adventure. PCs can adventure as long as they want, but as soon as they return and are awarded XP, they can't earn any more.
For example, if your 1st level PCs return from an adventure, and the DM tallies it so each PC earns 3250 XP, they can train. But the cleric and thief will each train for 2 levels (needing 3001 and 2501 XP, respectively to each 3rd level), while the others train for 1 level to become 2nd level, before moving on to the next adventure.