I'm a big fan of 1healer comps and I have ran Diene solo in the past. You can get away with Diene+3dps provided you have sufficient dps to just melt the boss before you incur too much damage. So something like wyv11, if your dps is strong enough it's perfectly fine to do this. Alternatively make your tank really beefy and have Diene heal him from the back. So in this case it would be your Tywin. For abyss and raids this is really sketchy. Diene needs to be on potion for certain fights like Queen. That's the danger of Diene solo, her healing with rod is mediocre compared to a real healer, and her debuff control with potion is like the absolute minimum you can get away with. To give you an idea in the past I ran Diene/F.Kluri/G.Aither/dps. Diene on potion because she's the only unit who can deal with debuffs, pre-nerf F.Kluri and G.Aither to keep the team healthy. I'll also mention that Bloodstone Bellona for these lategame PvE fights qualifies her as a backup healer.

You can get away with it, for awhile. I do think you will hit a wall eventually. You either need very high dmg relative to the content you're doing, or support Diene with pseudo healers like G.Aither/F.Kluri/Bellona. The problem with benching Angelica for Tywin is you have no healing so Diene will probably have to be on rod, then your debuff control is going to be pretty scuffed since you have only Diene's s2 to rely on, and your dps isn't even that high with only ML Tenebria qualifying as a real dps threat. Not to mention quite a few bosses heavily punish you for applying debuffs such as queen, council, and certain abyss floors.