An F1 team has to be run like a business. Its income stream is mainly from sponsors and the money the FIA give them.
Their expenses are vast and just like any business, if there is an opportunity to take part in more races then teams can charge their sponsors more money, as their brand names are going to paraded in front of more people.
Perhaps you are one of those mavericks who wouldnt want to run their team like a business, but you won't survive for long, as your income will quickly be dwarfed by expenses.
As I said, just like any business, if you have more customers/events/races/services (or whatever the business is selling), you hire more staff. It really is a simple as that.
All the larger teams have used this technique, which is why teams such as McLaren and Ferrari, who have higher budgets (read, income), are able to keep more staff on their payroll, as compared to the smaller/newer teams. This is exactly how businesses work - larger companies have more customers, so hire more staff. Conversely, smaller businesses have fewer customers so hire few staff. This really is elementary and I'm surprised this is even open to debate.
Regarding budget cuts: the teams would obviously have to explain to the FIA that if they decide to increase the number of races, then budgets will not be able to shrink to the same levels, previously agreed. This obviously would need to be discussed.