I always had these sorts of numbers in mind for myself actually - I reckoned I ought to be with somebody for at least 2 years before getting engaged, and at least 5 years before having (planned) children.
In hindsight it would have been really really sensible - IRL I got engaged and pregnant to XP after 9 months and it was FAR too soon - I had no idea what I was getting into. OTOH I got engaged with DH at about the 2 year mark and it felt about right. And by chance we started TTC at the 5 year mark, and I think we are pretty solid as a couple and seem to have struggled much less with the new baby thing than a lot of people do. Whether that's to do with the length of time or we were just lucky or because I already had DS1 so we already had experience of parenting together, who knows.
I do think it takes a good couple of years to properly get to know someone. And I also think there's a further level of knowing somebody which comes with a further few years of being together. It's probably not necessary to have these time limits in place, but it is sensible and helpful to keep them in mind, and to think about them if somebody is trying to rush things along without good reason.
If you are older than the point at which you'd be looking at potentially having your last planned child at 40, then obviously you'd want to reduce the timescales, but to balance this, you're most likely in your 30s, which means you probably have significantly more experience of relationships than somebody younger, and are more likely to be able to make a judgement sooner.
I don't think I agree with your 2 year deadline after a previous relationship at all, but there definitely should be a gap between living with someone again just because the gap allows you time to reset a bit, rather than potentially lurching from one unhealthy relationship to the next.