Not an uncommon occurrence for a two (or more) leg journey to have no Advance Purchase fares.
I've been looking at Taunton to Bournemouth for my sister and her friends. No Advance Purchase through fares but I can split at at Reading for two separate Advances or Bristol and Southampton for three separate Advances.
In the case of Walsall to Reading, CrossCountry don't offer any 1st Class Advance tickets on that flow. Only Standard Class ones. The fares database does have 1st Class Virgin Advance fares for Walsall to Reading. You'd have to travel via London with those though. I can't get any booking engine to offer that option for Sunday 22nd March though. Earlier dates do offer the option of a Virgin 1st Advance but the journey is heavily affected by engineering works on the
WCML▸ . No engineering work on Sunday 22nd March as far as I can tell, but also no 1st Advances via London. Perhaps they've not been released yet.
Choosing to split at Birmingham New Street and then buying a CrossCountry 1st Advance was probably the best decision.