I'm not sure if they have a clue, and as others said, this is more marketing than anything which - even if they did know better - is how political parties operate. Personally, I'd rather they focus on reducing cost of living so wages don't need to keep going up. They can't go up forever.
However, I wouldn't use Whitbread as any indicator of the hospitality industry as a whole at the moment. They had a shift a few years ago and little about them has to do with trying to remain in hospitality for the long term.
Their profits being down has little to do with the staff wages, and more to do with poor choices focused on wringing as much money out of the business with as little input as possible. They've continued to to raise prices well above value while there are other options, selling off some restaurants that haven't been maintained and so don't get a good price even if they were big names and changed some restaurants to hotel guests only which has kicked out local regulars in some areas, and now they're speeding up selling off many of their hotels to then rent them back.
They're making poor choice after poor choice, and the poorly paid staff are taking the hit - they've cut hours for cleaning staff to the bone and having their receptionists cover the difference alongside also being part of the restaurant side, which people have noticed in the decline in standards. That's why they're losing business, including reports that some long-term business contracts which made them a lot are being cancelled as businesses find other options - they're no longer value for money, in some places they're the most expensive option. They're also losing staff almost as quickly as Travelodge after the recent scandal and they've nosedived from an employer who regularly got accolades for being a great employer to one people tell others to avoid. Those at the top have been running things into the ground, and it seems fairly intentional at this point.
Why do people insist that every job should pay a living wage? What is wrong with young people living with their parents having a job that pays less than what's needed to move out and live independently?
Many jobs on or very close to minimum wage are jobs you want people with experience. As others mentioned, carers of the vulnerable are often on minimum wage. Teaching Assistants - often on or near minimum wage. Many of the staff in our court buildings - on or near minimum wage. There are so many others.
These and many like them have been at the bottom of pay longer than we've had minimum wage, and many of them - like Whitbread's hotel receptionists - are pushed to do more, often well out of their remit, because it's cheaper to squeeze the lowest paid staff to do as much as possible and give them BS 'appreciation' or 'Reward and Recognition' now and then. I've seen job adverts for primary Level 3 TAs at minimum wage that had them teaching classes and leading on an area of the curriculum, even the young adults who are Level 3 qualified and desperate for work know that's BS. And as others have said, this attitude affects most of the people up the chain until we get to the one's making these choices for their own benefit.
Also, minimum wage does not equal young people living a home, and those under 21 already have a lower minimum wage. There is also the issue that not all young people have parents to live with. As a pp mentioned, we can choose to support them through government benefits to live instead, but a lot of people loudly say that's wrong. The other option is businesses pay more. The option that lowers the cost of living is great long-term thinking, fully support that, but we'll need to cover the gap one of the two ways while we get there. This government - as have previous ones - can try both government support relying on increasing taxes and businesses paying more, and it's not working because as I said, we can't have these things go up forever, but like Whitbread execs, many politicians act in the short term based on the benefits to themselves and those that back them, rather than voters or those working for them.