I’ve tried a couple of automatic shift bikes (electronic, not mechanical) and the shift mechanism was so primitive as to be almost useless. On an automatic shift automobile, when you are coasting along and suddenly need to accelerate, you step on the accelerator and the gearbox downshifts to give you more power. I haven’t seen an automatic shift bike that does that, and I’m sure the Land Rider is no exception based on the description here.
If standard derailleurs are too much trouble for you (and I can understand that - they can only be shifted when the bike is in motion, and while pedaling gently), I recommend bikes with 3-speed internal gear hubs. They are very reliable and durable, and you can shift gears while the bike is stopped. They are common enough that most bike shops are familiar with them, unlike this Land Rider system. This Electra Townie has a 3-speed hub and a very user-friendly geometry (the pedals are further forward than on most bikes, so it’s easier to get your feet down), for around $330 retail - I would recommend something like that over the Land Rider. There are also 7 and 8 speed internal hubs, but the 3-speed seems to be the most robust and probably enough for most people. (There’s also one company, Rohloff, that makes a 14-speed internal hub - fantastic product, but very expensive.)