To answer your question, yes, you can simply remove the SSD and when you boot the system up, it will recognized the new cloned HDD as drive C: As for the benefits, a 2.5" sata SSD can perform 4 - 5 times faster than a spinning HDD.  An M.2 nvme SSD (on motherboard) can perform up to 20 times faster than a spinning HDD. As for the draw back, SSD is more expensive than HDD per capacity.  But you can install 2TB or 4TB of SSD when needed. Users are upgrading from HDD to SSD, you are on other hand are switching SSD to HDD. One TB of nvme should be sufficient to hold all applications.  It would be benefit to you to keep using the nvme drive and adding 2.5" sata SSD for games drive and large capacity spinning HDD for data.  Apps and games can load at the fast speed as possible while music, movie can play at constant slow speed. Only able to assist to solve your issue and provide information valuable to you.  The preference and choice are still yours.
I own an Inspiron 3910 desktop PC and I bought a new internal hard drive (with more space) to replace my current C: drive.  I cloned my existing C: drive to it so the next step is to remove my current C: drive.  I have the PC case open and according to the picture of the hard drive location for this type of PC ([URL] it should be on the front side of the PC near the top.  But when I look inside the PC I don't see the hard drive there.  I snapped the front piece of the case off just in case it was behind the metal but it's not there.  I'm looking all over and I don't see the C: drive anywhere. Obviously there is a C: drive - I am using this PC right now, and the This PC program shows it's there.  Am I crazy?  Why can't I see my C: drive inside my PC?
Inspiron 3910, can't find hard drive inside?