I have used external inputs periodically, but I usually get impatient with the bounces, so it's not the norm for me.
 
I have used them to apply RME Compression, EQ and Reverb to my mixes. It's a nice way to practice mixing a live gig. I sometimes mix live shows with my RME and my laptop, so it's nice to practice with those compressors, eqs and the reverb so I can get a good mix using the tracks I last recorded live.
 
I don't trust using touch live yet. I still use my mouse because I don't want faders jumping unexpectedly.
 
I do have a DBX 162SL Compressor that I usually use when tracking. I sometimes use it when mixing. Again, it's nice to be able to really study the sounds I get from the 162SL so I can be sure to pick the most complimentary settings for the material I'm recording.
 
I often record tracks I'm going to compress directly, then send them to the DBX, then use only the return signal from the DBX to mix into the monitors and mains (keep direct sound at -inf). That way, I can listen to the compressed track compared to the uncompressed track after the gig. And if anything should go wrong with the compressed track, I still have the uncompressed.
 
I often also record the send to the mains using loopback in the RME. That way I have a stereo pair that represents the actual way it sounded in the bar. This is good feedback after the fact. I can take my time to do a final mixdown and compare it with how it sounded in the club. That gives me time to review the various settings I chose.
 
I also save all my FX settings from the club so that next time I'm mixing the same band in the same club, I can just pull them up and pick up where I left off.
 
External Inserts are helpful for practicing with the gear I use live.

+1 for EI's.  I have a Symetrix 522 which is about 30 years old and is still working well.  It is a multiprocessor unit that has compressor/limiter, expander, gate and ducker functions.  It has two separate units which can be used as stereo or two monos or taking one side and feeding it into the other for two functions on a mono line.  The ducker works very well for me as I do narration with a music background. 

I use external inserts sometimes to hook in a Jomox T-Resonator or to send audio to the audio inputs of synths.

If Sonar's external insert were removed, then there are workrounds that could be used of course (though latency would need correcting for), but having the function makes things much simpler.

tlw
If Sonar's external insert were removed, then there are workrounds that could be used of course (though latency would need correcting for), but having the function makes things much simpler.

 
AFAIC Sonar and Apple Logic have the best EI plug-ins not just because of the overall functionality but because the I/O gain controls can be automated. This is very useful with distortion devices because you can automate the input to change the amount of drive. They're both really similar, except Logic doesn't have the phase invert switch.

 

Mosvalve
I sometimes use external inserts to output... audio through my old and trusty units Digitech DSP 256XL effects unit...

1)
That's what I'm using but I'm dumbfounded as to how to get the final mix mastered or exported.
I can hear the mix fine but there's no way to export it or record it real time into another wave recorder when its set up like this:
 
DSP256 OUT -> MOTU Line IN (3, 4)
DSP256 IN -> MOTU Line OUT (3, 4)
 
The External Insert window gives me these options:
SEND - Left MOTU Audio ASIO Analog 1-2
           Right MOTU Audio ASIO Analog 1-2
           Stereo MOTU Audio ASIO Analog 1-2
           (no mic/instrument or mix/return)
RETURN - Left MOTU Audio ASIO Mic/Instrument 1
               Right MOTU Audio ASIO Mic/Instrument 1
               (no stereo)
               Left MOTU Audio ASIO Analog 1
               Right MOTU Audio ASIO Analog 1
               (no stereo)
               Left MOTU Audio ASIO Mix 1 Return 1
               Right MOTU Audio ASIO Mix 1 Return 1
               Stereo MOTU Audio ASIO Mix 1 Return 1
 
The only way I was able to record the mix was to route the DSP's OUT to a mixer that connects to the MOTU and record the signal through the MOTU into Sonar on an audio track, but that seems silly. The whole process seems more trouble than it's worth.
 
2)
The above recording sounds good in Sonar but when I drag it out or Export it and play it in Media Player or any other wave player, that file sounds crispy, tinny and void of any bass, like I ran it through a high pass filter - EQ is way off outside of Sonar. This has never happened to me before.
 
Steve

My interface has a loopback input, "what you hear" in sound blaster speak.
 
That's what I do quick mixdowns with, just have a track named loop and I hit the record button when I need a mix.
 
If this were a 'real' mix I would turn everything into a wav and go through the mixing process.
 
 

2)
The above recording sounds good in Sonar but when I drag it out or Export it and play it in Media Player or any other wave player, that file sounds crispy, tinny and void of any bass, like I ran it through a high pass filter - EQ is way off outside of Sonar. This has never happened to me before.

 
This was apparently due to my system having a bad day. Several reboots and USB reconnections and the recording sounds right.

I've mostly been using external inserts for effects like H3000, SPX90, SDE_3000, etc. depending on the song.