However, yes, a LiIon battery is not meant to be left continuously on charge. A lead-acid battery (typically used in UPSes) is meant to be left continuously on charge.
Shouldn't the charging controller in the laptop stop charging the battery once the battery is at full charge?
It seems to me that a great many folks leave their laptops plugged in for weeks or months at a time, and that this would be something that a laptop designer would account for.
(Anecdata: The six-ish year old battery in my primary laptop still holds ~60% of its original maximum charge. This laptop spends the vast majority of its time on, with the battery installed, and plugged in to an AC outlet.)
Until I almost burned down my house. Aparently laptop battery charge controllers do not work as intended when plugged in for long periods.
Otherwise laptops are perfect as cheap low power servers.