As easily as you can block a message, so too can abuser create a new account.
Online harassment can be as persistent as in-person harassment - there's countless stories of people being continuously harassed. If it were so easy to block people online 'cyberstalking' wouldn't be such a big problem in the same area.
I understand many people rely on social media for professional networking but there's absolutely no reason why you have to use this professional networking account to trade verbal jabs with people on contentious topics, or confront trolls, or start political debates, etc. Make an alt if you want to slum it in the comments section. Again, this was common sense 20 years ago, and now seems like it's lost knowledge.
Seconded.
As the saying goes; "What is the difference between posting something on the internet and a tattoo on your arse?..... It's easier to remove the tattoo."
Because that personal information you posted or 'offensive' joke you posted when pissed will stay around forever to haunt you.
Because you can't instantly erase someone from your perception in person to person interaction. Online you can even proactively protect yourself, such as by adding words and phrases you don't like to your blocklist. Suppose I decide I don't ever want to interact with someone who still uses the word "retard". My computer can preemptively block those people on my Twitter, my email, even pages containing the word on my browser. It takes only seconds to wipe entire categories of people and opinion from every facet of your online experience.