The government paying for this is a good idea?
Bring in outside educators can be a very good idea if you're trying to teach specific skills that can be taught in a short time framework.
As for the cost, my concern with that is largely because nearly all of these programs seem to cost far more than they should. As KarlInOhio points out, whether the cost is reasonable is in large part linked to how many children are being taught and we don't have that information, but experience tells me that in most cases, these programs wind up costing about three times what I think they are worth (that's a personal opinion, but it's not entirely arbitrary - I've looked at how much the educators are typically paid compared to a teacher's salary for example - and I've taught such external programs myself and was paid nearly four times the hourly rate I get for normal classroom teaching. I took it, because it's what I was offered, but to a large extent, providers of these courses don't seem to be in a very competitive market, and schools and school systems don't negotiate that well to bring prices down).