Through a combination of internal and external factors, lithium batteries go through irreversible chemical changes on every charge cycle. Total charge capacity always trends down. Depending on a large number of variables, this might happen quickly or it might happen so slow you might never notice at all. It's all down to how and where the battery is used because temperature is mostly what drives the chemical reactions.
The other thing is that lithium batteries which have been deeply discharged below safe levels are permanently damaged. Just like charge cycle wear, this can be immediately apparent, or something that goes unnoticed forever, but the cell is damaged and will never be the same. Recharging such a battery can cause physical damage inside the cell.
Point is, batteries are chemical cells. They don't last forever because most chemical reactions are not perfectly reversible. Their specific application and environment strongly affects how long they last. But we do know conclusively that when lithium batteries are kept hot and charged and discharged at high current (such as in a handheld gaming device), they degrade faster. Cells which are kept at a stable temperature and low currents (such as headphones) degrade very slowly and can last a long time.
If you look past superstition, there's an entire industry that's been rigorously studying this problem for decades. There's a lot of literature and evidence.
Lithium cells do degrade. How fast they degrade depends on cell quality and environmental factors. It is, unequivocally, a question of when a battery will fail. It might well be a decade or two, but it will fail eventually.
I try to keep my cell phones as long as I feasibly can. Every single one I've used for more than 3 years has had its battery fail (as expected for a device that sees such heavy cycling). My current phone is on its 3rd replacement battery.
That said, this will get more important going forward, phone and tablet hardware updates get ever smaller and incremental, and longer software update cycles are another thing the EU is starting to regulate. So devices reaching 10+ might not be that unusual in the future.
And as an aside, the one type of battery that very frequently fail isn't the built-in LiPo, it's the good old user replaceable Alkaline AA and AAA batteries, and they don't just run empty, they leak and destroy your hardware in the process, even long before the expiry date and with charge left. It's so common that I am surprised that that hasn't seen any regulation or consumer protection jump into action. Using NiMH instead helps, as they don't leak.
And it was unnecessarily hard (actually dangerous due to fire risk) to replace it with a 3rd-party battery replacement due to excessive amounts of strong adhesive holding the battery in place.
The switch doesn't fast charge at absurd rates and generally has good thermals.