There would be 3 reasons for swapping out my double-chainring for a single-speed chainring and removing the front derailleur on my old schwinn world sport:

1. saving weight (negligible)
2. "if you don't need it, you don't need it" (a bike messenger-friend's mantra - if you don't really need something on your bike, get rid of it... it's just another part to get messed up. and I really don't need 12 gears for the commuting I do)
3. aesthetic (really the main reason - it would make my bike look a bit more unusual and a bit more clean)

Is there any real reason not to do it? The only issue I can really think of is with my chain-line, but as long as I get a small enough chainring, I could stay on my higher gears and the chain line should be generally ok.

As long as the chain line is pretty straight you won't have any trouble. Single chainring derailleur bikes used to be common. The nice thing about a 6-speed freewheel is that you don't get quite the angle spread from the smallest cog to the largest.

Worst case, if you decide you don't like it, you can switch it back.

Go with the big ring if you use it a lot now. But for converting you'll want to flip the big ring (or the "inbetween" replacement) to the inside of the spider arms. By putting your ring on the inside mounting points you'll ensure that it lines up more closely with the middle of the freewheel sprocket stack.

I did this similar mod on...started as a 12 speed road bike, converted it to a Fixed/ss, now I decided to make it a flat bar road bike with only 6in the back. Not sure what the cranks look like on an old worldsport, but I replaced my chainring bolts with some short stack ones and removed the big ring. Saved me the price of a new crank.
Here is a thought... and i might be off on this... if you are sticking with a 6speed, why not get the most narrow chain possible..minimizing that extreme angle?? However, I guess if the cogs are thicker than what chains can accommodate... you might have a problem??

The center of the stack should line up with the center of the space between the chainrings, so it shouldn't matter whether you put the single ring on the inside or outside position. The ring will be equally off center either way. Putting it on the outside will certainly look better. You may have to get short chainring bolts or shorten the ones you have. It's actually the female part (nut) that needs to be shortened.

You may have a problem with the chain dropping off of the chainring when you shift. There are various retention devices to prevent that, the cheapest of which is your front derailer.

The angle in the chain-line s caused by the position of the rear-cog relative to the chainring. The chain itself has nothing to do with affecting this angle. Wider chains are actually more tolerant of chain-line angles due to having more of lateral space to wiggle before the edge of the chain starts climbing over the chainring teeth.

I'm glad to hear this - I would definitely prefer to have the ring on the outer side of the spider for aesthetic purposes. I currently have 52t and 43t chainrings, I bought a 47t chainring to replace the two of them, as well as shorter bolts.

I'm concerned about dropping the chain, but I'm going to try removing a link from my chain and my hope is that the added tension will help hold the chain on the chainring. I would like to be able to remove the front derailleur.

I guess that YMMV depending on the setup but on my single speed coversion I did the inner position lined up nicely with the middle of the freehub.

Mind you I'd built it up with a crankset and BB that I had so it may not be the same for other cases. But a long flat ruler laid up against the ring mount points of the spider will soon tell the builder which side is more correct.