Car lead acid batteries were exempted as there is an existing recycling stream for them, and thus they almost all get recycled into new batteries ( leaving aside just how it works) along with most other lead acid cells.

And what exactly prevents doing that with lamps of all types?

And what exactly prevents doing that with lamps of all types?

People's laziness to go few meters longer than into regular waste bin...

And a bit more technical differences:
Lead acid batteries all have very similar construction and composition, they could be "treated" all in the same way. And even then, only the lead is what is reclaimed for the use in new products. It is the high content of relatively pure lead, easy to extract (so it become the cheapest way to get the lead for the new battery making), what make the lead batteries so attractive for recycling.
And most important, the recycling infrastructure is set up and running already for decades...

Lamps are of too many varieties, each of them requiring separate plant in order to be efficient in reclaiming all valuable materials in usable quality.
The content of all the valuable components is only minute, while vast majority of mass being forms of glass and metal. While the toxic components tend to react with the surrounding materials, what make them more difficult to extract, so the recycling of old lamps is not the cheapest way to get material for new lamp making.

Then instead of stupid bans, should have invested in setting up recycling system for lamps, and include a purchase fee/return value system

Then instead of stupid bans, should have invested in setting up recycling system for lamps, and include a purchase fee/return value system

The problem is, than the safe recycling of lamps is expensive, you would need separate process for nearly each lamp family, while the value of recoverable material is rather low (valuable materials are in tiny quantities, while the cost of the abundant glass is mainly in it's processing - so recycling can not save on that).
So this activity would never be commercially viable, so it would need heavy funding. Moreover it would need strict separation of the lamp types,  e.g. fluorescents would have to be separated according the phosphor type (tri-phosphors vs halophosphate), if the rare elements should be recovered (how could regular user do that?) So up to now the all "recycling" effort was limited to just get rid of spent lamps so they won't damage the environment. But that is not the real recycling...

On the other hand recycling lead batteries is extremely simple: Crush, rinse out the acid, let the plastic float, smelter the lead and pour it into molds for new batteries. As with this you may recover >98% of lead into new batteries, while the process is quite cheap, it is commercially viable to recycle the old batteries without extra funding.

So add fees to the lamps accordingly, to fund recycling with them...

So add fees to the lamps accordingly, to fund recycling with them...

This is done. But it is difficult to update the fee so, it follow the cost per lamp. The problem is, than  the cost per lamp strongly depend on the amount of lamps used in the market. As the market shrinks, so do the recycled amounts, but the processing have quite high cost unrelated to the processed volume. So when the market become below some threshold, the fee would "skyrocket"...

But still, even with such fee, if people are willing to buy that product and so pay that fee, there is no right to ban that product.

But still I'm convinced, than that would mean the end of the lead containing wood glass products anyway, as the fee would make them not competitive against the lead free competition.