Your view is an accurate view. It takes the end user -- be it some sort of client, browser, or manual user retry -- to hit the other, alive IP(s). There's also the TTL of a bad record being dropped to consider.
You can simulate IP failover with something like Elastic Network Interfaces / Elastic IPs in AWS... it's just not going to be on the same level of speed as doing it in, say, your own rack in a datacenter. It's also subject to weirdness where you could have some sort of split brain, nodes trying to take over interfaces in a loop. The health checked "multiple load balancers behind a single DNS record" approach has flaws but also simplifies a lot of things.
You can simulate IP failover with something like Elastic Network Interfaces / Elastic IPs in AWS... it's just not going to be on the same level of speed as doing it in, say, your own rack in a datacenter. It's also subject to weirdness where you could have some sort of split brain, nodes trying to take over interfaces in a loop. The health checked "multiple load balancers behind a single DNS record" approach has flaws but also simplifies a lot of things.