but the "Remain Clear" bit does come over very frequently indeed
This is probably because, through experience, if an ATCO
doesn't tell an aircraft to remain outside controlled airspace, and that aircraft subsequently enters CAS without a clearance, the ATCO is treated as being equally at fault. Simply hoping that pilots will comply with the rules no longer applies.
GA transits of CAS are rarely a problem, and are made far easier if the pilot states their intentions clearly, reads the clearance back correctly, then complies correctly with that clearance. A transponder also makes everyone's life easier. Having worked at a unit with instrument approaches in Class G and seen plenty of GA aircraft fly through the final approach at the same height as the approach profile without working the unit concerned, I would always advocate the Class D airspace I work in now.