I see two cases of the Philipines variant have reached the UK. .........
I think you're right, the new variants are likely to cause us grief for a long time to come. The longer the pandemic goes on across the world the more likely it is there will be new variants, and we know full well what the result can be from the "UK/Kent" variant (which is what is causing the 3rd wave on the Continent at the moment).
Many countries have even more distrust and suspicion of their governments than we do (often for good reason), and lack of trust is behind a lot of the reluctance to accept what they are being told. It's so difficult to build trust and so easy to wreck it. I think the suspensions are demonstrations of caution by the governments just to try to build some trust and confidence in the populations, it's basically an unfortunately necessary PR exercise. I suspect the suspensions will be lifted once a reasonable "consideration" period has passed, too soon and it will look like another fiddle. It costs lives, but stuff happens in the real world of politics. Screw up the lifting of the suspension and the governments lose all credibility.
All governments have made mistakes in the last year, we are beginning to find out just how big and expensive some of those mistakes have been. Unfortunately it's not a rehearsal.