Well surely this is an extension of education, at school I had to choose between a bunch of options I wasn't that keen on and forced to take compulsory subject which I hate.
There is some value in the idea of getting people a little out there comfort zone. This was the practice of a college I went to. If you were academic then you had one afternoon a week doing something totally different (I did forklift driving, Indian head massage, photography, and a few other things). Similarly if you weren't academic then you got extra support to boost your English, maths etc.
If national service is framed as an extension of education, and credit is given for it then it would be more worthwhile. I don't see how you could run this that cheaply though. Realistically you would need to provide accommodation and food etc. for it to be a valuable experience then it would likely need to be away from home. I suppose you could take over some of the university halls where university's have over reached and are now in trouble. You would need to pay a stipend of some kind although it might be in cash terms low to account for the accommodation and food. Or it could be voluntary but in exchange for another benefit ( reduced repayment rate for student loan?)
This needs to be part of a bigger societal plan with, department structures and budgets being adjusted to cater for this. With places offered in sectors
DEFRA: there are thousands of miles of pathways, fences, canals, forests, rivers etc which could be maintained, wildlife to be monitored etc
DoE: educational assistant
Local government: lots of roles could be looked at
Civil defence force: military/ police/ fire etc
The headache is that many people and unions would feel like this is replacement of roles, also thousands of existing job descriptions would need to be changed