Technical side. Alkaline cells have a long shelf life, great for emergency use. Any kind of rechargeable will "decay" slowly after every charge, there is no guarantee they will be ready for you when you need them. They also have lower output V, and my understanding is that they also hold less power capacity. For example, Alkaline AA will be around 2500 mAh compared to NiMH at 1200-1900 mAh. I'm not talking about lithium because they also have their own problems and special circuitry required to charge cells, monitor temperature, etc..., adds cost and complications.
There is a purpose and usefulness for each type of battery. They all need to coexist. I agree that we should try for rechargeable when practical. For example, many toys and radios now use them. Computers and cellphones and now cars on various forms of lithium batteries. Great. But certainly "one-use" should never be banned. Recycled yes, but we need these batteries.
If the problem of "throwing away in landfills" is bothersome, perhaps battery companies can incentivize recycling by putting a "deposit" on each battery or providing a credit towards a new pack of batteries, like they do with empty bottles and cans. Right now battery drop-offs (and other eWaste) are found in lots of big stores like Staples, BestBuy and so on.... but there are no incentives to do so. I would love to raid the dumpsters of these eWaste bins... Likely more than half the stuff can be easily repaired or pieces cobbled together from different machines to make a better one. But rather than allowing hobbyists to "refurbish" these and get "down-cycled" (reused by people who don't need the latest and greatest hardware, put Linux on the machines and keep them as plug-in-only laptops, etc), they get sent to China or Pakistan to get picked apart by people without any safety protection and get exposed to all sorts of hazardous materials. I know down-cycled stuff will still end up being thrown away eventually, but it will at least delay things and prevent people from buying even more stuff. Obviously manufacturers don't like that, they would rather see you dump things every few years.