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.)