I'm not sure that I can give any good arguments, since I have a local database on my laptop. And, yes, it is a copy of production.
But that is all up to how you work in your team. Depending how sensitive the data is, this can certainly alone being blocker for having copies on a developer laptop.
On the other hand, if someone is going to work on a bigger development task which requires changes to multiple tables, there is all reason that this person gets a sandbox isolated from everyone else.
Obviously, the change that the developer makes on his or her own laptop has to be propagated to the main dev server at some point, but I take for granted that you have all database code under source control.
If the development team does useful, complex and effortful work, then I do not think that you should reject such request unconditionally.
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