well, what do you mean by "other jobs"
Are you saying a supermarket cashier should be paid the same as a doctor or a lawyer or a police officer?
nobody is denying minimum wage jobs are important and necessary. But some jobs are both important AND have a lot of responsibility AND require a lot of training.
In some places you can get more working as a cashier for aldi than you will for your first year as an ambulance paramedic - which one has more responsibility, requires more training and is more important to society?
We are never going to arrive at a completely fair society - if we were then carers would be paid more than footballers. It's probably easier to think of it within the same sector rather than comparing apples to oranges.
Nobody (or at least nobody decent) would argue that minimum wage jobs deserve to be paid well, or at least fairly. The point people are making is that there should always be an incentive to work at the 'next level', otherwise people won't bother.
If you are a consultant you should be paid more than a junior doctor, to reflect your added experience and additional qualifications and responsibility.
The same applies if you are a supervisor in a supermarket, you should be paid more than a cashier. If you are in overall charge of payroll for a large company you should get paid more than the new starter who does the basic admin. If you are a teacher you should get paid more than the teaching assistant.
But repeated increases to minimum wage without corresponding increases throughout the rest of the organisation mean that people start thinking 'hang on why am I doing all this extra work, have all this extra stress and responsibility and am paying back a fortune in student loan, for what works out after tax as 10p an hour more than my colleague who doesn't have any of that?"