So, there is still useful capabilities when adjusting non-raw files like jpegs but overall, the more you can take care of starting from th raw file, the better.
I would also add that a lot of the processing in ACR/LR for non-raw files really depends on the source of the file and what color space and gamma the rendered images are in. A camera JPEG that is sRGB or Adobe RGB will not fare as well in processing as a Photoshop 16 bit RGB image. The ACR/LR processing pipeline is based on doing the processing in it's own color space which is essentially ProPhoto RGB colors with a linear gamma in 16 bit. So the closer your rendered file would be to the pipeline, the better the processing of the image will be.
Look, processing an image inside of ACR/LR that started life elsewhere is still a useful strategy...arguably better than processing the file in Photoshop. But the closer that image is to raw, the better potential for corrections down the road.
If I were to rank the alternatives to raw, the 1st best alt would be a linear DNG. It's not restricted to a fixed color space and the linear gamma gives a lot of head room editing the extreme highlights (a benefit to raw). The next best would be a ProPhoto RGB in linear gamma, but that's not something that's easy to do...a ProPhoto RGB 16 bit would be a slight step down from ProPhoto Linear. Less good would be Adobe RGB 16 bit...the ARGB color space would clip potential colors and the gamma is already locked in at 2.2 so you would lose precision going from 2.2 to linear.
The worst source of files for editing in ACR/LR would be sRGB or Adobe RGB camera JPEGs...and it would be pretty low on the ladder compared to raw. But compared to opening an sRGB camera JPEG in Photoshop for editing, ACR/LR would still be a better processing pipeline.
I don't disagree that some 3rd party Lightroom plug-ins that render the raw file into a TIFF can be useful. The key point is at what point you go into the render format and why. If you've already done all the image corrections in ACR/LR and need a processing routine you can only get via the plug-in, go for it. You'll still have your original raw file you can go back to.
The vast majority of my images always remain in raw format. The only time I render a raw to a 16 bit ProPhoto RGB is to do those things that can only be done in Photoshop–and I always do this so I can soft proof and do final retouching prior to making serious prints. Note however, once I've rendered the image into Photoshop, I rarely go back and apply any Develop module image adjustments...