well, they will be paying tax on it if they save for any longer than a year....which is, generally, the whole point of saving!
If the 'young person' (and given we're talking anyone under 65, they don't have to be that young) is earning over £50k, then they will be paying tax on any interest over £500
First year, £12k in an ISA, put "the difference" (£8k) into a normal savings account, at 4.5% (which is currently the highest rate on offer for easy access = £360 interest. Fine, no tax.
Next year, put another £8k, plus the original and interest = £16360. Assuming they can still get 4.5% interest, that year the total accrued interest will be £736.20, so will get taxed at 20%.
So they'll start paying interest after only about 20 months.
Come the third year, and every year after, even those who aren't higher rate tax payers will go over the £1000 interest rate, and be taxed 20%, which you wouldn't if the whole £20k was in an ISA.