I used to work in Sales & Marketing and my employer used to pay for training courses, including providing that training on a working day - thus paid for my time - and also paying for lunch (though may have been included by the training provider, but even then it's part of the package, so is still paid for).
That knowledge gained by attending training courses I still use today, so it did benefit me, as well as my employer.
If an employer can afford to pay for training, including the employees time for attending that training, then I feel they should do so.
What you need to consider is the costs involved. The amount you save under the voucher scheme, may be around £1000 a year. If you spent £1000 a year on your employees training, then you have no gain from the voucher scheme. Now a first aid course won't cost £1000, typically a first aid course (12 hour) will cost around £80, plus be two days worth of your employees time. You could also through in lunch expenses (say £10 per day). You may also want to pay for travel expenses. I expect it would cost in total say £300. If you gain £1000 via the scheme, then you are still £700 up. Registration cost under Ofsted vOCR is currently £100, so that drops your remaining amount down to £600.
Does the person you have found already have Common Core training suitable for Ofsted registration? Can be hard to know, as Ofsted are not issuing a list of courses they accept! (Can you tell I've moaned to them about this on numerous occasions.)
If you are starting from someone with no training at all, then the first year costs of providing that training, the time off to do that training, and registration cost could result in you having little left over from the savings you make by using the scheme. However, Year 2 will be different.
You need to talk with her to find out what she wants you to pay for. She may be happy if you pay the course fees, but not pay for the time/travel/lunch.
Personally as a nanny, I pay for my own training courses. My employer pays for the annual registration.