The advantage of letter pairs is that you are able to encapsulate two pieces with a single image. A few very ambitious people have actually gone to a person-action-object memorization scheme. This means they have memorized 500+ letter pairs for all three categories: a person, an action, and an object - so a total of 1500+ letter pair words. By doing this, a single image of a person performing an action on an object can hold 6 pieces. And the other nice thing is that the order of this interaction is enforced because it is always in the order person-action-object. But it takes a great deal of work to come up with non-overlapping words for all the persons, all the actions, and all the objects, so it's a really big investment to learn this. I would love to try it someday, but I will need to wait until I have a lot more free time than I do these days.
I can see where you might think "Tiger Singing" is as easy to memorize as "ToaSt". And if you're just talking about that single image, you're right. But once you start stringing them together, you are generally trying to put together some sort of picture that holds several of these images. So if I needed to memorize TSPEBD, I would imagine a slice of ToaSt being PEeled (like a potato, with a peeler) on a BeD. But you would have to memorize something like a Tiger Singing to a Potato that has been Electrified when a Butterfly that is Drifting lands on his nose. It's a lot more elaborate, and will reuse those words often from solve to solve (the thing that Keroma12 was referring to), and also it takes longer to think through when refreshing memory.
Also, while I'm sure you're currently just targeting single pieces, if you do continue with this, eventually you will in fact be moving to having separate "algorithms" for each letter pair. Intuitive 3-style really isn't all that difficult, and you don't actually have to memorize the algorithms to be able to use it - you merely have to be able to see how to do them in your head. With not too much practice, you can get where you are able to see them pretty close to immediately. Proper 3-style with optimized speed algorithms takes tons of practice and will probably never be practical for old slow people like you and me

, but 3-style with simple commutators isn't that hard to learn to do without specifically memorizing every single one. For edges, you can actually progress from M2 to pair commutators by applying a few simple optimizations that work for many of the cases and are very similar to the original M2 algorithms you learned before.
As for old and slow, I just turned 60 and I'm still able to do kind of okay with BLD. Like you, I prefer bigger BLD. And Mats Bergsten is still on here and is 12 years older than me, and yet is about the same speed as I am at BLD. So take heart, you can make more progress than you think - being old is not a barrier.