The lock-downs imposed in (2) countries were very effective and given a bit more time (and political will) they could have transitioned to strategy (3).

Australia and China managed to do this.

The lockdowns imposed in countries that only used them to prevent the hospital system being overwhelmed were very effective on average, but that's not enough. In order to reach Covid Zero you need lockdowns to be very effective everywhere. Take for example the UK - there were apparently some areas where cases kept growing even during the strictest lockdowns, and that's enough to ensure you'll never reach zero cases.

All the countries where this worked seem to have the advantage of being geographically and geopolitically distant from Italy, which meant they could take action against their outbreaks at a relatively early stage before they got deeply embedded in society. (Early on, cases were more or less a gradient radiating out from Italy, probably because they had a major outbreak which went completely undetected as in literally reporting zero cases country-wide despite having an awful lot more than that.)

If I look at the center of Amsterdam, in the past year there have been losts of tourists from all over Europe even when bars and restaurants are closed. So this means that any strict lock down would have to be coordinated at least within the EU.

In the past, EU countries did not want to delegate health care to the EU (except for approving medicine). So this would require lots of individual countries (including Sweden and, until this year, the UK) to suddenly agree on a single strict lockdown. Very unlikely to happen.

China actually had a bit of advantage here, as other countries started shutting out Chinese nationals, preventing their citizens from going abroad and reintroducing the virus. Also it seems like as the first hard hit place its citizens started to become wary of traveling abroad earlier.

You don't have the right to even smoke in a restaurant now, what's the right issue when talking about a health issue here. It needs the same reason as quarantine requirements being imposed on people. So many 'we are different' refuse to stay at home and wear masks.

The real tragedy is that most of countries are following UK and US as their model because most of their government policy makers are trained in US and US, and they don't have the capacity and courage to set out their own plans.