Sure, but what if the motherboard (or some other proprietary and expensive component) has a major failure? Then you're stuck with a locked CPU.
Generally, the used market values standard form factor stuff more, so you'll frequently see people running a supermicro/etc server with a low end CPU wanting to upgrade to a better CPU from the same gen. So, pulling CPUs to sell to the enthusiasts in the used market from proprietary servers (HP, Dell, etc) when they go EOL has been pretty standard practice for at least a decade. There then ends up being a big pile of undesirable proprietary motherboards/chassis, and low-end CPUs for them. Both eventually get e-wasted, sometimes with the motherboards/chassis getting parted out.
The reasoning for this is pretty simple. Shipping an entire server is expensive - at least $100 CAD, sometimes more. Shipping a motherboard is cheap (sub-$30), and a CPU basically free (~$10). A proprietary server cannot be upgraded down the line (whereas a standard SSI-EEB chassis can have its motherboard swapped for a newer one), which decreases its value further. If someone has a standard chassis, they can buy any standard motherboard; to sell your proprietary one, you have to find someone with a proprietary chassis and a dead/missing motherboard, a very small market (supply vastly outpacing demand). For someone to want to buy your proprietary whole server, they'll have to be willing to accept that the chassis is junk whenever they want to upgrade past its generation of hardware, which is a relatively small market. Resale value in a few will also be terrible, because no one wants old hardware they can't upgrade. The market has a pretty hard cap on value for old hardware. All of this put together means that proprietary whole servers are worth (maximum_price_for_used_server * proprietary_undesirability_multiplier) - (shipping_cost), while a standard motherboard is worth (maximum_price_for_used_server) - (shipping_cost) and an unlocked CPU is worth (maximum_price_for_used_cpu) - (shipping_cost). It can sometimes be the case that selling an unlocked CPU from a proprietary server nets more money to the seller than selling the entire server, depending on era/brand/specific CPU.
Plus, shipping a motherboard is much more difficult and expensive than a CPU.