No.
I don't know of restaurants around here that actually does large bookings (think special rooms for example) that would cancel in October for a Christmas party and give the reason of staffing. Could it happen due to unforeseen circumstances right before the intended event? Sure but they have to weigh the odds of canceling that because it does not give good PR and they typically make more money on these. I've been to a fair few of these work outings with my husband's prior company and then so far only one event with my husband's existing company. Admittedly they drop serious cash when they do so even when it's 16 people plus their spouses/significant others for a project outing or a decently sized larger work party. Obviously not every company does but a lot of times these places have either a booking/space reservation fee, packages required, etc.
The OP talked about restaurants with off-site work Christmas parties occurring there so that's what I was talking about. For example Fogo De Chou their system allows you to make a reservation for 14 people and it's counted as normal reservation. If you need more than that it shifts to a group dining booking under a different process with different things such as packages. Using my husband's present company they have about 100 people here (much smaller than my husband's prior company) and Fogo De Chou for a weekend dinner would cost without alcohol $6,936. They would never not have alcohol so let's do 2 drink tickets like they did when they rented out space at Chicken and Pickle (a place that you can play pickleball among other things). Now the cost is $9,282. Now mimicking the Chicken and Pickle experience they had several hours of food plus a bar serviced and staff to restock the food and staff to walk around picking up empty drink containers. That type of experience at Fogo De Chou for 100 people would be just about $10,100. That's just one example, there are places less expensive and places more expensive for sure. Drop the figures even to half or a quarter and it's still a decent amount.
There's staffing issues around here but like I said the places here that have space for a larger group typically place those as higher importance. I'm not talking about you taking X number of your family members and asking or even reserving a table of X. I'm talking about specifically booking a place for an event like a company calling in saying they are wanting to book space for their employees.
I can understand a restaurant shutting off the capabilities to reserve future events in anticipation of issues continuing.