Could it be because the costs are immediate but the benefits are long-term and so will not bear fruit for decades? I would be truly shocked if it wasn't. One of the problems with health care being a major political issue, even though almost nothing changes whoever is in charge, is that long-term benefits that have significant short-term expenses are very unpopular, since the government in charge won't benefit from giving the go-ahead. Then again it could simply be that giant bureaucracies with little to no incentives to improve things are generally dysfunctional and can't tell their ass from a hole in the ground. Probably waiting for the costs to come down even if overall the savings are significant.
I think it’s partly cost and lack of experience. But it might mostly be because these injections are biologics which suppress your immune system, controlling the asthma but leaving you at higher risk from infection.