Yes, this would lead to the legislature spending a lot of time just reauthorizing existing legislation, but I would argue that the majority of new legislation being passed in modern representative democracies would be better off as revamps of existing legislation anyway.
https://www.mercatus.org/bridge/commentary/idaho-repeals-its...
Sunset provisions are a pain for anyone who administers the law or makes plans for the future based on it. Laws that depend on the current date are bad, and stable legal institutions are good. That’s why we incrementally “reform” the law, rather than periodically replacing it like some depreciating asset.
We already have govt shutdowns when we can’t pass a budget, imagine if a law that legalized gay marriage was allowed to expire, or one that granted people health care or immigration status.
Even if a non-discrimination law only expired for a short period of time, that would be enough to do real damage to people’s lives.
When a civil rights law sunsets, lots of bad can happen in a short period of time.
I’m using the example of the government unable to agree on a budget as an analogy.
What happens when we can’t agree on how to renew the Civil Rights Act and it sunsets for a period of time?
A mandatory sunset provision can only work if the legislators act with the interests of their country and constituents first and their individual pockets second, which isn't the case any more in many Western democracies. The US are just the most obvious example where Republicans blocked everything Obama tried to pass through.
You could also reduce the risk by the constitution itself being exempt from sunsetting and enumerating crucial rights and services therein.
Anyway it's not something that's ever going to be implemented anywhere, so it doesn't really matter if it could work.