I technically have dual nationality for UK/Ireland. I’ve only ever had a UK passport, but am an Irish citizen and could get a passport if I wanted.
I have applied for Irish citizenship now for my kids so they have EU membership as the eldest in particular is looking at studying abroad.
The only worry I can see is that if you are a citizen of a country, that countries rules apply to you. So if you are imprisoned in that country, the UK embassy can’t help, as you’re an Italian/Irish citizen. Not so much of a worry in european or western countries, but I believe this is part of the issue with Nazarin Zaghari-Ratcliffe, as she holds Iranian nationality it means Britain does not have the diplomatic sway they would have were she just British.
As for irritations in the process, the paperwork! Birth certs, death certs, marriage certs, all original. Certified copies of passports and photographs, which can only be certified by certain professionals who have known you at least two years. I had to send both kids, mine, and my parents documents.
Plus every man and his dog are discovering their heritage in an attempt to maintain EU membership. Current processing time for ireland is 12-18 months instead of the usual 6.