There isn't a "glut" of delivery drivers. Demand is high and supply is low. It's hard for firms to find delivery drivers, especially for any vans bigger/heavier than a normal car licence, and especially for anti-social hours driving, such as overnight.
Hand car washes, nail bars, Turkish barbers, ethnic convenience stores are often more about money laundering, illegal working, modern slavery, etc., and aren't really anything to do with what they're actually doing/selling as they're just "fronts", so irrelevant when talking about the job market.
Healthcare and social care IS a massive problem, mostly caused by low pay and low respect, plus poor working conditions.
But, yes, we do need a "job audit" to actually look long term at where the shortages are going to be, what jobs will be created and what will be lost, over the next 10/20/30/40 years, and work backwards right back to the schools, to change the way we educate our future workforce whilst they're children, to provide relevant and required training for 16-21 year olds which must include far better provision of trade/manual/vocational skills and probably reduced academic/university choices, a return to our once World leading adult education sector so that people have more options to retrain once they've left formal education, at whatever age they are. The whole system from age 4 to 21 is a mess and still based on what we needed several decades ago, not what we're going to need in 10/20 years' time. And a new initiative for adult education, retraining, re-skilling, etc is an absolute essential and we literally can't start that soon enough - far too many people in their 20s, 30s and 40s are pigeon-holed because of their school qualifications and prior employment and are just "fodder" for the lowest paid and lowest respect jobs.