To note, this isn't always true.
My family moved to Portugal in late 2020. Covid played havoc as they had to find ways to digitalize many things their offices were doing. It took my wife 9 months to get her DL exchanged and me 11 months.
During that time, you are not driving illegally; you are driving from your foreign license. As long as you have the paper with the exchange info and a picture, you will be fine.
It also helps if you hire a relocation expert who knows the system. We paid ~$1,500 to a Portuguese American lady who helped us with everything. She handled setting up all our health care, apartment negotiation and contract review, set up all our utilities and phones, all our residency paperwork, DL exchange, bank account, and more. I highly recommend her and any group like her. They know how to work the system. My mom does similar back in the USA for newly arrived expats for companies.
Covid was a real shock to office-heavy organizations; it has been a mad scramble to change culture, paperwork, operations, etc. I think they are doing decent and hopefully, in 5 years, it is night-and-day difference.
I've lived in Egypt as well... the bureaucracy there worked really well (before revolution). I just had to go to a giant building and spend half a day there, done. Sure I had to taxi to a DSL place to pay, but that was pretty easy as well.