My favorite "load balancing" for web-pages is using "DNS round robin" where you add several A records, and the browser automatically try another IP if the request fails.
The browser tries another IP if it cannot connect to the first one.
If a server throws 500s left and right DSN RR won't help, whereas a load balancer would remove the offending server from the pool.
DNS round robin is not failover. If one of your four A records points to a dead box, 25% of your customers are SOL.
Browsers even try other IPs and alternate between IPv4 and IPv6 before the connection is established.
The whole point of it is to connect to multiple A and AAAA records with a very short delay (250ms in chrome). The browsers use poll to get notified about the first established connection and then use it. So if one A/AAAA records IP is unreachable or slow it will use a another one. There will be no fallout (except maybe for clients that don't use something like happy eyeballs, but any browser does that) if you have multiple A/AAAA records and one of them is down.
We deploy to production several times a day. We have an in-house product that our own emplyees use and they absolutely love that they can ask a feature in the morning and get it in a few hours (in best case scenario). That wouldn't be at all feasible if all those deployments caused errors to users. Luckily that's not a problem, because these days it's really easy to get zero downtime deployments with all this containers and "serverless" functions and whatnot.