is it really "always" or is it just taking more time? what is happening in the background is that you are downloading a file that is more than 40 MB in size and it can take a while depending on your internet speed. you can find the file here on windows: %appdata%\Electrum it is called blockchain_headers
as for upgrade, you are not switching wallets from one implementation to another like what you did with Multibit to Electrum. you are just getting a new version of the same implementation which is from 2.8.2 to 3.2.3
the only thing you need to do in this case is to have your SEED backed up by writing it down on a piece of paper. sometimes it is best if you make a copy of your wallet file too before making the upgrade but SEED is more than enough.
the process is downloading the new version installer from the official website, then verifying its signature, and if it was valid then simply install the new version by double clicking on the installer (for windows, in Linux simply replace the old files with the new ones that you get by extracting the tarball).
~ I have heard that there are HD wallets being made, and importing private keys is not possible anymore.
you don't need to import private keys for upgrading but just so you know, it is possible to do it. it's just that Electrum is preventing you from importing a private key in an HD wallet (a wallet that has seed) to prevent you from having 1 key among other keys that can not be recovered from seed while the rest can! so it forces you to create a separate new wallet and import that 1 key there so it is obvious that this key is not recovered by your HD wallet seed.