It's a very common mistake, and SE didn't do a very good job at explaining this one. The descriptions you find on each physical spell are the same you'll find on WS descriptions; i.e., they only apply when you use the spell AS a WS, consuming TP. Ergo they only apply when combined with Chain Affinity.
This is not to say "holding TP" is bad in every case. For spells that "Damage varies with TP," you'll notice a significant difference between 0% TP and, well, anything higher. A good example of this is Cannonball; when using SATA Cannonball (usually on popped mobs like sky gods), it's very common for the BLU to build up 300% TP prior to ensure maximum damage (thus, maximum hate boost). In Dynamis, I've toyed with using CA Vertical Cleave (alone, not with Expiacion) on BLU/SAM, and I'm pleased with the results.
Keep in mind that whenever you self-SC, your closing spell will only cast with 0% TP + whatever TP you got from the WS. Closers with "Damage varies by TP" (Frenetic Rip, Hysteric Barrage, Vertical Cleave, Cannonball) tend to be a little lacklustre, and Savage Blade + Disseverment (which has "Accuracy varies by TP" instead) tends to be the best.