USB-C vs USB-A Lightning Cable For iPhone 13

I just upgraded to the iPhone 13 and the store employees were stating that using the Lightning --> USB-A cables from my older phones will ruin the new iPhone 13 batteries over time (so instead of using any of the older Lightning --> USB-A cables and wall bricks I have everywhere, I needed to use only the new charging cable provided with the new phone and purchase new USB-C wall brick adapters to work with the new cable). Is there any truth to this? I am reading here in the communities that the older connectors will work but if so, why are we being told by retailers otherwise? I just want to make sure I get the best out of my investment and not ruin it early by using incorrect charging cables.