As a southerner who lives within an hour commute from London I shall explain why towns and cities that will be within an hour of London will benefit.
As I have said I live within an hour of London (and always have done) yet most people where live do not work in London, based on train passenger numbers at most 25% of all people where I live use the rail services (which is the main method of travel to London for work given the drive would be significantly longer and less reliable, that 25% is assuming each passenger from our local station lives within the settlement and they use the trains 400 times a year, twice a day for 200 days). However, even then that doesn't account for the significant numbers of people who are traveling to the settlement or from the settlement to other nearby settlements by rail (either for work or education and there's significant numbers who use the trains for college), nor does it account for those from nearby who drive to the station to travel by train but aren't within the settlement's population. Although, conversely, it also doesn't account for those not of working age. Either way it is a LOT less than 50% of people who could be working and almost certainly is less than 50% of those who are working.
I have never worked for a company in London, but often travel there for meetings. As it allows me to have cheaper travel costs and shorter travel times day in day out but still be able to attend a 9am meeting within London as needed.
As such, if that is a workable pattern for many businesses in the Southeast, I expect that a similar pattern would then follow suit for cities served by HS2.
Often the problem for businesses isn't getting the brightest and best or even finding office space it's finding the admin staff, the junior staff and the cleaners. By moving to an area where your staff can be in London quickly (even if it is so they can go to the theatre after work) whilst you can find all the staff you need and have much cheaper rents the business is likely to thrive more than being in Central London.
Therefore, given that more business will be able to be based in the provinces doing what many of the companies in the Southeast currently do I would say that HS2 would be good for those areas. In the same way that Basingstoke, Farnborough, Swindon, Reading, Guildford, Brighton, etc. are all thriving towns with many people traveling to them for work (as well as for leisure purposes) rather than traveling to London.
In fact, other than for work purposes I hardly travel to London and so most of my personal spend is local to where I live, with a small amount being spent where I work). This is also true for those I know who do work in London.