Full range drivers with piezoelectric tweeters

Back in the late 50's while experimenting with optimization of my first system I tried using a RadioShack piezoelectric tweeter to enhance upper frequency reproduction. From my perspective today I'm sure I would find that setup marginal at best but the enhancement of upper frequencies was significant.

Since then, piezoelectrics haven't crossed my mind. However, over the years I've read and heard discussed the advantages of full range speakers based, I suppose, on the lack of a requirement for crossover circuitry. This makes sense to me and I decided that I want to experiment with this concept in a small setup in my garage. Based on information that I received during at least one discussion, though, it seems that not all "full range" drivers are very upper frequency capable.

This is where the question of piezoelectrics comes in. Based on my understanding that, by their nature, they cannot reproduce low frequencies (what these limits are I still have to determine), a crossover is not necessary which would give me more latitude in choosing a full range, or woofer in this case, driver.

For the purpose of this experiment I have an old but decent pair of bookshelf speakers that that I would remove the tweeters and crossovers from and parallel connect the piezos across the input terminals. This is the way I connected it in my original system over 50 years ago.

The concerns that I have are related to impedance issues and the division of frequencies between the two. In effect, the woofer would always be reproducing all frequencies that it is capable of and the piezo would always be self limited to frequencies above a certain cutoff. So there would be, indeed, a potential gap or overlap with no slope control.

I'm not asking for a detailed analysis or driver recommendations; I just want some idea of whether it is conceptually viable and if this approach is ultimately inconsistent with the goal is the full range speaker idea.