The spell Plane Shift allows a character to travel to different planes. RAW, is there any reason I can't use the spell to travel to the pocket dimensions, say the pocket dimension of my familiar?
Nothing prevents plane shifting to an arbitrary pocket dimension except acquiring the appropriate material component: “a forked, metal rod worth at least 250 gp, attuned to a particular plane of existence”.
Getting or tuning the the fork to match an unknown (and possibly unknowable) plane is either a prohibitive challenge or a potential adventure arc. The DMG's notes on the spell (p. 46) spell this out more explicitly:
The plane shift spell has two important limitations. The first is the material component: a small, forked, metal rod (like a tuning fork) attuned to the desired planar destination. The spell requires the proper resonating frequency to home in on the correct location, and the fork must be made of the right material (sometimes a complex alloy) to focus the spell's magic properly. Crafting the fork is expensive (at least 250 gp), but even the act of researching the correct specifications can lead to adventure. After all, not many people voluntarily travel into the depth of Carceri, so very few know what kind of tuning fork is required to get there.
The knowledge needed to craft a tuning fork that would work to plane shift into a specific pocket dimension is nigh-impossible to acquire (DMG, p. 68, “Demiplanes”):
Theoretically, a plane shift spell can carry travelers to a demiplane, but the proper frequency required for the tuning fork would be extremely hard to acquire.
If getting to a particular pocket dimension mattered enough to actually pursue at all costs, just learning the correct fork construction details would be the culmination of an epic adventure — more epic than going to the depths of hell!