Yes at Chudliegh there are a few open caves. On the far side of the Kate brook Cliffords is well worth a look and you should also have a look down Skullcap. On the other side Pixies is an important bat roost so gated but Bruces rift is open and good fun.
Not far away is Kerswells, this is open, but fairly small. As Les said keys for Bakers, Afton and Radford can all be sourced from DCUC (they will post them to you). Those 3 are all locked due to land owner requirements, and for the first 2 DCUC has tenancy agreement with the landowners (we actually pay rent for Afton) to enable caver access to be allowed. Reeds is controlled by the Pengelly and is owned by a wildlife trust, is an important bat roost so once again, is locked and a leader is needed, but its not difficult to get one. Dog Hole again needs a key. I'm not acutally sure what the reasoning is behind locking it, but DCUC can supply a key.
Anyway I can see the fustration but if you do have a bit of notice there is no reason why you cant get access to nearly every where.
Andy