One option would be that headquarters remain even as organizational workforces scatter. There will always be a need to at least occasionally hold meetings or access resources or project a presence in a major city. Cities would like this as headquarters are a status symbol.
Another option is that headquarters move to locations more central to their workers or more attractive for workers. This is more unlikely but the same factors pushing workers away from major cities – high housing costs, traffic and congestion, density with threats of pandemics – could affect headquarters as well. It could be a big strategic move to follow workers to a city not on the list above.
The effects of either could be big for cities. Consider New York. It is the clear leader in terms of headquarters, it is a leading global city, and it is not just a center for business but also for news, entertainment, the arts, and other spheres. Even if the headquarters stay, the loss of high-status employees hurts. If the headquarters leave or become shells of themselves, there could be a loss of status.