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Lithium is a valuable and expensive metal.

A pouch battery like an iPhone is worth about $4 in lithium. Those big 20 amp and 30 amp portable bricks are worth nearly what you paid new to a specialist buyer/refiner.

Boardsort has reasons for no longer wanting them. And most yards are generally reluctant to keep them around.
Hell, tug the arm of any top level manager at a cell phone store and they’ll tell you they don’t like having spares around in bulk.
When all goes well, great.
Any minor issue, problems. Police and fire department problems.
And scrap yards have nightmare level issues on record. Just look up the videos on YouTube. Or head off the normal track and look up the scrap yard that had the guy torched and 3 people died.

Look, truth, in your phone there’s not much to worry about. Those portable bricks (the quality ones) are reinforced with shock absorbing plastics and titanium or hardened steel shells.

but when you have 500 of them and one slips off and gets run over by a 20 ton fork lift… the battery bursts into jet fire, the tires catch, the propane tank explodes, and you have 10 tons of shrapnel and flaming goo.
Which is why so many recyclers want nothing to do with them.
And that’s aside from the fact that something like 99% of people don’t tape the contacts. Short fires are a common menace.

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Occasionally I cut off the connectors from laptop and cell phone batteries. If they have separate wires you can safely cut it off, but if they have thin ribbon wires I would not attempt.

Some laptops (such as mid 2010s MacBooks) have a BMS board attached that's a small high peripheral board

Everything else goes into the Call2Recycle battery bin at Home Depot or wherever. I can't find any scrapyard nearby that buys batteries, I understand that they are probably a fire hazard to store especially that not everyone is responsible enough to tape the terminals.