>"aluminum conducts heat more rapidly AND evenly than Ti. "
As Bob Gross mentioned in his response, yes, Al heats more evenly than Ti, but not more rapidly.
Evenly: The greater thermal conductivity of aluminum and the typically greater thickness of Al versus Ti pots, provides a bigger "pipe" to move heat through the pan bottom from hot spot over the burner to a larger area of the pot bottom. Consider high-end kitchen cook wear and there is a thick disk of aluminum imbedded in a SS pot to provide that uniformity across the pot bottom (alas, not UL at all).
Rapidly: Nope. The limiting step in heat transfer from flame to water in a pot isn't the pot. The thin, highly thermally conductive metal – whatever metal it is – conducts heat very well with very, very little temperature differential across the thickness of the pot bottom. The next slower step is conduction into the water. Here we are aided by the heated water convecting off the pot bottom and being replaced by cooler water. If your gloppy dinner is too viscous (lentils with little water, mac&cheese, etc), not enough heat is conducted/convected off the pot bottom and you burn your dinner. We've all done it. We try not to in the future. But the slowest heat transfer step is the air film outside the pot. Heat fins help with that, a lot. Anything that disturbs the airflow (like vortex generators on a airplane wing) help somewhat.
Pot weight has a small effect on heating time – you do have to heat up the pot, but the heat capacity of 100 grams of metal is 22%-26% that of a 100 grams of water, and none of us carry really heavy pots, so it is a small factor.
If you think one metal is heating up water faster than another metal, something else is going on. Small differences in pot geometry, tightness of your lid, surface finish on the pot (shiny metal doesn't emit much infrared which is good for the upper pot sides, but bad for the pot bottom that sees LOTS of IR from the stove burner), or the interaction with a windscreen is different between them.