Is scanning 16 bit TIFF old negatives worth it?

I am looking to get my old c-41 35mm negatives scanned and most labs are providing 8 Bit TIFF only. Some people say that there is more posterisation effects while working with 8 bit mode so it benifits to work on 16 Bit TIFFs.
But I have also researched that we can also work on 8 Bit TIFF with 16 bit mode on photoshop to prevent posterisation. So I am thinking what are the benifits of TIFF originally scanned at 16 Bits?
And if there are benifits like for example more "original" color depth data, are they really worth it?

It depends on your subject matter and the final delivery media/medium.

Subjects with many fine, continuous graduations of the image tend to suffer more from unwanted posterization when manipulated in lower bit-depth image files.

A seemingly unrelated book, "DIGITAL COMPOSITING FOR FILM AND VIDEO" By Steve Wright (Focal Press) goes into detail behind the mathematics that tend to cause banding and posterization in image files that are less than 10 bit color depth.

I highly recommend obtaining a copy and reading the chapter on bit depth and image banding/posterization. It is well worth the effort and you don't have to purchase the latest edition; buy the older 2nd edition and save some money!

With older C-41 negatives, there will probably be enough grain and/or scanner noise to prevent banding. I have only had banding issues from low resolution scans.

Nevertheless, since I do my own scanning, I tend to scan in 16 bit mode, make basic adjustments and then convert to 8-bit to save disk space. Important scans I will sometimes leave at 16 bits.

If you have a lot of rolls to scan, you could have them all scanned in 8-bit mode, and if you have problem negatives, you could have them rescanned in 16-bit mode. I doubt you will have any issues.