I am a licenced and bonded landlord and will answer from that perspective.
You do not say where you are, however, within the U.S. States that I operate in, there is little in the law about bugs with some obvious exceptions.
One exception is infestation. While there are varying degrees of concerns with infestations, the landlord has one obligation and that is to remedy the situation within a reasonable time using reasonable means. This often means hiring a licensed exterminator within a reasonable period of time and solving the problem within a reasonable time. This does not always work. For example, ants and termites may require additional expertise in solving the problem.
Centipedes are often a result of moisture. While spraying is a start, the management may have other issues such as cracks in the foundation. Even small ones are enough. This is a prime example of requiring additional expertise. It may be that additional work is required. Centipede are common and largely harmless and often do not constitute an infestation. They are creepy for sure.
Regardless of what the lease says, the law prevails here. Only a few rights can be waived by contract.
The landlord is required to use all reasonable means to solve the problem. Until it can be proven that the landlord has failed to solve the problem using reasonable means, you have no legal recourse.
You can certainly ask to have the fee waived. However, the landlord is under no obligation at this point and may choose not to. It is your choice. However, I would make sure you are not on the ground floor if you do switch apartments.
One other thing. There is no such thing as just one roach. The landlord should be spraying adjacent apartments including above and below. As well, assuming there is a basement, the landlord should be paying attention to cracks and gaps there too. Roaches require water and food. If another tenant is not clean then that is a problem that the landlord must solve also. This may not be too alarming of a problem since most roaches come from tenants moving. Higher turnover often means more problems including bed bugs. Proper periodic maintenance is required for larger apartment complexes.
Use this answer as a standard by which to gauge the landlords response.