Geez....I hardly know where to begin.
Quote from the OP's opening question: Is a hobby lathe suitable for turning items under a 4-5" in diameter with any accuracy?
The answer is a resounding "yes"! The statements about lightweight machines not being that accurate are completely false and misleading. Both Sherline and Taig make very small lathes and mills and many machinists use them to make extremely accurate parts. Here's just one website to illustrate this.
ModelEngines.info
That's a fair statement to a point and that point is the little machines also take little cuts. You can't take any appreciable cut because the machines become 'flexible' from delflection. Little = little cuts. Most home machinists have the need and regularly hog even if they aren't familiar with the term....
I'm sure for some, "hobby" can mean full size machines. But how many of you have ever lifted a 10" 120 lb rotary table up onto a Bridgeport to make that specialized little 3 inch round part? If you don't mind making weightlifting part of your hobby then have at it. How about an appropriately sized vise for that large table? Expensive and heavy. Hey, you say, you can always put a smaller RT or vise on the table but we're talking full size production quality stuff now, remember? Get the tools that fit the machine.
One does not need to purchas a large rotary table or indexing head or milling machine vise. I have a Troyke that weighs way more than 120 pounds. I also have a small one that weighs about 20 pounds. It's economy of scale and what you use the tooling for that determines the overall size. Both tables are happy on the vertical mill....
The cost of the tooling that goes with the lathe or mill no matter which size you buy will exceed the cost of the machine itself, by far. Best to keep that in mind.
Someone mentioned why not get a Bridgeport. There are many reasons not to. Not the least of which is you need a forklift to move it anywhere and it better be on a concrete floor. Affordable, used Bridgeports are often well used (read OLD) and in need of reconditioning, not something for someone wishing to start a hobby making small parts. Do you need 240V for it? Or a phase converter? Count me out, and most other hobby machinists as well.
My comment is that most B'ports that are used will need ball screws but replacing intrinsic parts gives the owner a 'feel' for what's inside and how it works. As far as utility (electric) bills go, it's cheaper to spin a 240 volt motor over a comparable one thats 110 and 3 phase (if you have it) is even cheaper per KWH than single phase and a capacitor banked static convertor that will run a 3/220 B'Port costs less than 100 bucks new and is the size of a box of cereal.
This is like asking for advice on which tractor to get when you only have one acre. There's always someone out there who will advise you to buy the Case tractor because bigger is always better. Not.