Re: Lifetime warranty
The HPE warranty check typically displays the end of warranty about 100 years from the date of manufacturing.
My experiences are very similar to you, though I remember HP stating that for 4000m modular switches (ancient stuff) they would ship replacement cooler for free only one time. The switches had been working for 15 years until then and another 15 afterwards was very unlikely for such noisy Fast Ethernet stuff with only a couple gigabit interfaces.
There's also a fleeting chance that you'll receive something much more modern when that 10base-T switch finally dies...