To be fair Delta is a very different beast from Omikron.

The virus is mutating so the government strategy has to adapt too. Elimination was an option for a while.

Elimination stopped being an option the moment the first infected carrier left Wuhan on an international flight.

Not necessarily; the first few carriers don't seem to have successfully seeded outbreaks, in general it takes a few attempts to get a disease like Covid established, and almost all countries seem to have stopped it spreading directly from China including closely-linked ones like Taiwan but also places like the UK and US. As far as I can tell something just went really badly wrong in Italy that no-one is interesting in examining too closely, and when this spread Covid to other countries it was spun as proof the other countries had screwed up and failed.

Temporary local eradication was an option for a while, before delta: see Australia and New Zealand.

However these countries were always going to have to open up and accept the virus eventually as it became endemic in the rest of the world. They were just delaying the inevitable. As it happened, the evolution of the virus made the decision for them. However if Delta had not happened they would still have had to make the decision to open up at some point, probably after a significant proportion of the population was vaccinated.