Does it makes sense to apply feature scaling on timestamp
For time series analysis.  Yes

But, turning data into a computable object for using in the ML computation?  No

Using the data as a feature.  Then, Yes

I would give you a general time series example:

Consider the number of days in months. The irregularity causes friction while analyzing the model.

Consider this:


So, such type of transformations would be helpful which analyzing time series', which can help reduce friction in the models sensibly.
Link of the explanation