Great Western Coffee Shop

No doubt the answer is 'because of reasons' but trying to book a single journey from Walsall to Reading (change required at New Street) on 22nd March in 1st class offers me a 1st class anytime ticket for ^119.50 (vs standard for ^21.10).

Or I could just take a ticket to New Street for ^3.30 (no first class available on this local service) and then snap up one of the 6 remaining tickets in 1st down to Reading for ^33.80

I chose the latter option.

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.  ;D

Just out of interest (and perhaps rather naively), are there any splits that will get me from Reading to Plymouth any cheaper than a "single" ticket?

I'm totally showing my ignorance here, I'd always thought split ticketing was where you had multiple tickets for what is a single continuous journey and not where you would have had to have changed trains regardless.
eg, on my up journey I've split Euston to Birmingham at Rugby.

You're unlikely to beat the Advance Purchase or Super Off Peak Single price. There maybe options to beat the Anytime Single if travel has to be on a weekday early morning.