It's a can of worms. Are you talking type 1 SPD or type 2? Best practice is certainly to have a way of disconnecting/servicing them without shutting down the panel.
There are different classes of SPD, including ones which may be connected directly to service conductors, ones which may be connected just downstream of the main breaker and ones which must be protected by a branch circuit breaker.
The first type does not require a disconnect either, but having a disconnect would make it easier to maintain or replace it in the future. The added impedance of wiring in a disconnect would reduce its ability to mitigate surges.
Look at the mfg instructions. I install Levition 32,000 and 42,000 series, they require a 30 ampere disconnect.
The 52,000 series are a feed thru type, power wires land on a bus, in and out, this makes a very low impedance connection, the BC breaker is the disconnect