I don't feel that accurately reflects what I've said. But I understand that you don't like a paladin moving further away from being a typical caster.
It isn't a matter of liking it or not. It is a matter of the compatibility and the power of the class as a whole. Just as yet another example, currently Paladins work with the multi-classing rules, with their spellcasting and smites operating under that system. Making a piety point system that works like the 4 elements monk (which as a system was largely panned for how bad it was) would throw that completely off and need to be addressed.
The "extra power would need to go somewhere..." No, because that had been addressed in previous comments. Still, you don't like it, so okay.
Even if kept a small list of spells, you are now casting without casting. Creating all of these potential problems, and limiting the number of spells paladins can even possibly know.... and again the sole benefit seems to be "keep Divine Smite from being a spell". Which is just not worth that amount of effort, especially when the designers already considered it to effectively be a spell.
As for the balance issue, most of the issue was that the paladin didn't have a limit to stacking damage like other 5e classes do. If that was the only issue, there was no reason to change paladin at all; just errata how often Divine Smite could be used.
That was not the only issue. It has been stated repeatedly, on this thread and in the interviews with the designers, that they ALSO wanted to bring Divine Smite in line with the other Smite Spells. It was not only the stacking of damage on multiple attacks, it was also that Divine Smite costing no action type made all the smite spells that cost a bonus action far too weak. It was also that Divine Smite technically not being a spell meant it could be used on the same turn a paladin or a sorceadin used a bonus action spell, while the smite spells couldn't be used that way. It may have even been an issue that Divine Smite couldn't be counter spelled and could be used in an anti-magic field, while the other smite spells could not.
As long as Divine Smite worked completely differently than the other smites, they could not be effectively balanced against each other. And that made those other spells useless.
By the same token, taking a spell like Glimmering Smite which has the potential to cancel invisibility and grant advantage to every attack against the target for 1 minute with no save and making it ALSO cost no action and ALSO able to be used the same turn you quicken cast a Fireball... would likely be TOO strong.
To accomplish their three goals (keep the paladin as close to the 2014 system as possible, reduce the power of Divine Smite, as well as raise the power of the other smite spells and make them viable options compared to divine smite) they chose what seems to me to be the most effective and least disruptive option.
Could you have accomplished a similar set of balance concerns by making a piety subsystem that has the Paladin not-casting spell-like effects that are uniquely listed as non-spell options, in a mix between the 4 elements monk and the sorcerery point system? Yes, you could have. But that is not an easy conversion, or one without deep concerns for how the system functions. And the only design goal it accomplishes that the current design does not... is make paladin different for the sake of being different.