That is basically true, but it depends upon how useful your skillset is.
If you have experience and skills that are rare in the EU - say a training captain on a rare type, or a test pilot, you may well still be employable and a company will help you get permissions to work there. If you're a 300hr fATPL with type ratings on common stuff like 737s and A320s (or none at-all) frankly, that's probably not you. Same applies to a European with an FAA licence (of which there are many).
On the other hand, the study and training are the same, you can do the flight tests with a single examiner: plenty are dual qualified, ditto medicals, and the only real differences if you plan it right are two sets of very similar written exams, duplicated paperwork, and a few thousand in additional authority fees. And the position may change going forwards about rights to work.
So I would still do it (and whilst I got my licences before the UK left EASA so it was a bit easier for me) and did do, in my case I fall somewhat into the rare skillset category, although to be frank the extra time and effort hasn't paid for itself yet. My personal decision is that I'm keeping dual licences and ratings current until the end of 2023, after which I'll re-assess, and if the EASA licences haven't actually been very useful by then, will probably let them lapse and keep them in my back pocket to revalidate if reasons re-emerge why I need a current EASA licence.