I have no direct experience with slate countertops, but having chosen another material (marble) that has its lovers and its detractors, I would simply state that this is a completely aesthetic decision as long as you go into it with your eyes open.
I've read that slate is non-porous but others will attest to water spots. My parents had slate floors in their old kitchen and I do remember once every 2 years or so we'd have to clear out so they could re-seal them. Not sure why that would be necessary or recommended if they were so non-porous. It could have to do with acid etching (more on that later) but I don't think sealing protects against etching. It's not as hard as granite and is likely to get chips, dents, and/or scratches. (Remember, even granite can get chips - my parents have granite and one corner of a peninsula is missing a little pea-sized chunk.) I'm also not sure what finishes it's available in - if you can polish it like you can granite and others.
IMO, from a utilitarian standpoint, it is hard to beat granite or stainless steel as a countertop. They are durable, essentially totally non-porous (I know granite is technically porous but when polished, as a practical matter, it's not going to absorb anything), and easy, with a simple wipe, to get to a perfect mirror clean. Ditto for most of the quartz materials.
But I think marble, slate, soapstone, and others are a far superior aesthetic choice in many (I would say nearly all) home environments. They will get scratches. Honed surfaces don't shine up quite like polished can - from an angle, in the light, I can often see the lines of where I've wiped the counter down unless I go to great care. I believe slate will etch with acid - which means lemon juice and spilled wine, evey tiny droplets, will leave little imperfections that you will similarly see in certain lights. This may cause the water spots some talk about. These warnings drive granite aficionados nuts. If you're the kind of person who wants a perfect, brand-new-looking space forever, granite or quartz is your best choice.
However, if you are willing to simply accept some of these imperfections as patina and the trade-off you simply have to accept for the aesthetically superior material, then it is a fine choice. For me, having accepted these trade-offs, I'd say slate is a wonderful choice.