There's a few practical issues with what you suggest for filling the gap though, a gap that's already there and already causing issues with many areas being short staffed.
As others have said, there's people's level of capability to consider, mental health, education - not everyone can cope with a 'professional' career for a variety of reasons.
When it comes to students, those in families who need a supplementary income, people who have other jobs - employers want full flexibility, for a zero hour contract you're often expected to be available at the drop of a hat and across the whole week, and if you're not because you have children at home and the main breadwinner is at work, or you're at college/university a chunk of the time, or at your other job, they'll just not give you any hours, or you don't get the job in the first place because you're not available enough.
That isn't an usually issue with retired people, but then their age can be, younger workers are cheaper and more likely to be naïve and put up with stuff someone who's done a professional job and now retired won't, because they know they don't have to. I've worked a few places where age bias when recruiting is a thing even though it's very much not supposed to be, where they're very reluctant to hire anyone older or retired because they're usually over qualified on paper too, despite their motivation for applying. There's also the physical aspect of it in something like hospitality or retail where the job can be very physically demanding and the recruiter thinking they wont be able to keep up.
Then there's the issue of customer demand, and the demand for better and better service from places like hotels and shops, look at all the complaining around at the moment about lack of customer service. People want consistency, they want people who know what they're doing, they are demanding it.
You don't get that from a fragmented work force without a core of people who provide that consistency and experience to deliver a good service.
So yes, I agree people's expectations need to change, starting with employers who expect fully committed and available staff for a zero hour contract, poor working conditions and the least they can legally pay, and consumers who are all for losing experienced and committed staff so they can have a 'better' job to fulfill their life with homes and children, and be considered 'worthy' of such things, but also demand high service levels and people who know what they're doing.
Brexit has caused some of these shortages because of the loss of migrant workers, and business is failing to respond to that by investment in their own work force.
I agree with you regarding care work, however the same attitude still does prevail and that's what has led to the shortage alongside the loss of migrant workers. Care providers are too used to cheap labour and higher profit. Most traditionally low paid industries are very similar.
The over riding attitude is that it's lazy people causing the problems and although there will be a selection in any society, companies and services are failing to invest in the very thing that they rely on to keep going - their workforce, instead prioritise profit (under the guise it's good for everyone, but not everyone sees the benefits) and then the societal attitude is 'Get a better job if you want better pay' instead of investment in the services we all want and need to ensure that there are people available and willing to do them.