GNU grep, the most widespread implementation, does not include egrep, fgrep and rgrep for years. Distributions (not all, but many) provide shell scripts that simply run grep with corresponding option for backward compatibility. You can learn this from official documentation.
It seems you need to read the official documentation yourself. While it’s new information to me that egrep is no longer a symlink, as it used to be a couple of years ago, but a shell script wrapper to grep -E instead, the egrep command is to this day still provided by upstream GNU grep and is installed by default if you run ./configure; make; make install from source. So it is not a backward compatibility hack provided by the distribution.
You can check for yourself. Download the source from ftp.gnu.org/gnu/grep/grep-3.11.tar.gz, unpack and look for src/egrep.sh or line 1756 of src/Makefile. Apparently the change from symlink to shell script was done in 2014, and the deprecation warning was added only last year.
In any case, my larger point is that the depreciation of egrep was a pointless and arbitrary decision that does not benefit users, especially not veterans like myself who have become accustomed to its presence. I don’t mind change, but let’s be honest, most people are not in the habit of checking the minutiae of every little command line utility they use, so a change like this violates the principle of least surprise. It’s one thing if things are changed with a good reason and the users do not only suffer the inconvenience of the change but get to reap the benefits of it as well, but so far I haven’t found any justification for it yet, nor can I think of any.
So if there is a portability problem with using egrep now, it’s a self-inflicted portability problem that they caused by deprecating egrep in the first place.
Also, my scripts are not full of bashisms, gnuisms, linuxisms and other -isms, I try to keep them portable unless it is really necessary to use some unportable command or syntax.