I don't use any external hardware synths.  Everything is a software synth.  I'm trying to get a handle on best practices for that set-up.
 
I am really struggling to understand why anybody would ever use what seems to be the more popular method, creating separate MIDI and audio tracks and then routing the MIDI into a synth, then the output of the synth into the audio track.  It seems about 1000 times easier to simply insert an instrument track.  As far as I can tell, this achieves the same result with much less clutter.  You can put all the same audio effects on that track and do all the same automation.  Where is there any benefit in doing it the long way around?
 
I have been doing some arrangements with as many as 9 or 10 instrument tracks and this has been working great.  Almost no drop-outs and the latency is not a big problem.  I have not seen any need to freeze tracks.
 
I tried it the other way this afternoon (splitting into separate MIDI and audio tracks).  Not only was this far more cumbersome, it seemed to consume twice as much CPU power for the same exact voices, and this causes frequent drop-outs with most of the different synth modules.
 
All the posts I have read seem to imply that the "proper" way to do this is with split tracks.  My guess is that is the old way of doing things, and old habits die hard.  I can't see a single advantage to that method -- and am at the point of concluding it isn't even viable on my computer hardware.
 
Is there any advantage that I am missing?  Why would anybody ever split tracks when they can simply insert an Instrument Track?

The Simple Instrument Track works fine if you have a single non-multi-timbral synthesizer being driven by a single MIDI track. And you don't mind losing a few of the controls.
 
But if you're seriously into software synthesizers it's only a matter of time before you'll run into the limitations of the SIT. You may want to overlay two patches, slaving a second synth off the same MIDI track as the first. Can't do that with a SIT. You may want to use a multi-timbral sampler such as Kontakt for convenience and better CPU efficiency. Can't do that with a SIT. 

There are some problems/oddities with instrument tracks, like one I discovered the other day in which cloning an instrument track results in a track whose mix controls are all linked with the original track.

But other than this, if you're having no problems with them them just keep using them. I also feel that a lot of the people who swear by split tracks just do so because old habits due hard. For 95% of cases of using VSTi's I think there's no reason why having split tracks would be better than a simple instrument track. You're right, they're so much neater and more convenient. Can't say I've noticed any difference in performance though.

One day however, you might find the need to do something different like process the left and right sides of a synth's stereo output differently, and for this it's worth knowing how to set up audio tracks with synths by the more conventional method.

All of the above, plus I'll add I like the organization of having them separate. I put all the synth audio tracks into a folder at the bottom of the project. This way I can MSR them as a whole. Then I put the MIDI tracks into folders grouped by instrument type (DRUMS, BASS, GTR...) Often times I'll have separate parts of the same synth that I'll keep on separate MIDI tracks for ease of workflow when arranging which helps tremendously. In music like electronica, where you tend to write by building up huge arrangements and then trimming down this is great. 
 
That said, inserting a synth is a pain becuase you have to do a bit of organizing, and bouncing down is a pain because you have to select both the MIDI AND the audio track (srsly, I wish they'd fix that). 

Drums - can never get them just right in a single stereo track. That's plenty of reason to split them out into multiple audio tracks.

bitflipper
slaving a second synth off the same MIDI track as the first.

Aha.  I didn't think of that.  Thanks.

I don't use SIT for all the reasons given above - multi-timbral synths, multi-out drums, organization, etc.
 
 

sharke
process the left and right sides of a synth's stereo output differently,

That's way beyond my skill level at this point, but I can see that could make a difference.

SuperG
Drums - can never get them just right in a single stereo track. That's plenty of reason to split them out into multiple audio tracks.

Can you please explain a little more about that?  Do you send them to two different synths?

Many drum VSTs have multi outs - separate outs for kick, snare (top & bottom), overheads, room, toms, etc.
Each will typically have different fx added to them - comps, eq, verb "wetness".