In my experience, this ("you will end up with very contorted routes") is not necessarily the case. That said, component placement is definitely something of a black art. Given 4-layer boards can be 10x the cost of 2-layer boards, IMHO it's at least worth trying. (For that matter, I've run into instances where trying to turn a 2-layer board into a 4-layer board just made things worse, at least with THT boards that turn all layers into Swiss cheese.)
It's true that with through-hole it's easier as you can route many traces under resistors, even adjust their lengths or place them vertically, and bridge distant traces with 0Rs.
If you stick to SMD, and if you're not allowing yourself super-fine traces, it becomes really hard pretty quickly.
In both cases with single-layer layouts you often spending lots of time placing, rotating and re-placing components. Maybe if you master the black art you can do it very quickly, but when I do it I generally end up having to cheat by adding a few jumper wires to finish the design. Planar graphs are rare.
Do you have examples of heroic single-layer artwork?
If you don't have too many constraints (size and such) I believe two layers with vias makes things almost always routable (even if ugly), and you spend 1/5th the time compared to single-layer work. With 4 and 6 layers I think basic routability stops being the main issue, you can place your connectors and components in a sensible way, count on at least one good ground plane and focus on other issues such as parasitics, thermals and avoiding stupid footprint mistakes.
I'd second that, but it depends on the component. This works fine for basic stuff like resistors, capacitors and transistors. Not so well for relays, and I wouldn't recommend pure-surface-mount for terminals.
For external terminals especially heavy-duty ones such as screw terminals I agree. For low power internal or board-to-board connections that will only see a few mating cycles SMD should be fine. If you look at a PC motherboard you'll see that lots of connectors are SMD.
With home-made PCBs I use 0.1" SMD pin headers, they take up more space and are not as robust but I prefer that to drilling 40 holes. Also, edge SMA connectors are pretty mechanically robust if you solder them on both sides as you should.
SMD versions of some connectors sometimes have a plastic peg or notch that fits in a hole and provides mechanical strength against pulling. You only have to drill one hole. For example there are DC power jacks.
For prototyping, soldering some wires to pads is the easiest.