The real worth of a die filer was for filing dies requiring "profiling" and adding a relief angle to that profile. The video, while showing off the Oliver die filer, did not (at least in my opinion) do justice to, nor did it show the real work a die filer is meant to be doing.
I have a die filer in my own shop, a bit lighter than the Oliver that the OP here has. I use my die filer for its intended purpose. Truth to tell, if I have to "break the corners" on a piece of stock or on a piece of work, I do it by hand filing with the work in my bench vise. On the other hand, I had a job recently enough for which the die filer was ideally suited. A steam engine governor had badly worn "pawls" on the ends of the two lever-arms which have the governor balls on them. These pawls need to be identical in profile. The wear and loss of material on the pawls was horrendous. I was unsure of the material the pawls were made of (cast iron vs steel), so built up the worn areas using aluminum bronze brazing alloy. I rough profiled the pawls with a bastard file. I then dowelled both pawls together as a stack, and filed them to the original profile, with both pawls filed simultaneously. The die filer was the ideal machine for the job, as I had to profile the radius'd end and relief on the pawls. A fine-cut file in the dies filer (thanks to Maynah for sending me some machine files) did the trick. The die filer did a fine job, and the last step was to polish the pawls on a canvas wheel with some buffing compound to take off the file marks. I had no other means or re-profiling the ends of those pawls other than maybe making a mandrel and using a rotary table on my Bridgeport to generate the radius'd ends. I use the die filer for profiling various shaped small parts.
Where a die filer comes to the head of the class is for putting relief or draft (angling of the sides relative to the faces) on parts such as dies of patterns. With the table set at the appropriate angle, this is easily done. On blanking dies (for cutting a part out of a sheet of metal or other material), some relief on the blanking die (angling down and away from the cutting face) is needed. This is one of the uses die filers were intended for.
As an old timer, I was came up in the era when learning how to file was a standard thing. The result is some work like putting a chamfer on the corners of a job, deburring, filing an edge flat and square, are all stuff I just do. Using a die filer to do the work of a hand file or belt sander (chamfering the end of the round aluminum stock), seems like more trouble than it is worth and almost a mis-use of the die filer. I keep a "hoof rasp" at my bench. Once side of it is a very coarse bastard cut flat file, the other is the rasp. I discovered that for roughing down edges and faces on jobs when I do not want to run them in the milling machine, the bastard cut file on a hoof rasp really takes off the metal, even A-36 steel. I follow up with a finer bastard file, then a second cut file. In many cases, this combination of hand filing is quicker than monkeying around to set the job up in the mill, and the die filer simply is not the machine for that work.
I use the die filer for finer work, and work I cannot easily do, or do at all, by other means. Using a die filer as a scroll saw or to cutoff stock is well and good if no other means exists in a person's shop, I suppose. Clamping a fairly large file with the tang sticking up and using it with the top section un-supported in the die filer strikes me as not a real good idea, if not unsafe. Die filer or machine files are made with the faces and edges all parallel. Files for use with handles are generally tapered in both directions along the run of the file. The exception to this are "pillar files" which have parallel faces and edges. The file the OP put into his die filer hardly looked like a pillar file, and likely had the tapered faces and edges. A die filer needs files which have straight and parallel faces and edges in order to work properly. A file for hand work, having tapered faces and edges will have the work pushing in and out against it as the file strokes up and down. It also may not be held too well in the chuck, designed for parallel files.
One of the sources I have found for round files that work in die filers are chainsaw files. These are true cylinders over the length of the file with no taper, unlike a rat-tail file.
A die filer is intended for fine work and was never intended to take off any great amounts of material. I use my die filer for fine work when it seems like the best or only means. It is not a machine for hogging off material or roughing out jobs. I find that for profiling some jobs out of steel plate, I can drill holes, use the bandsaw, and then either use the Bridgeport, or hand file with coarse files to rough in a profile, finishing with finer files. For one-off jobs with odd shapes, or jobs like the governor pawls, the die filer is ideal and I do not use it for rough work.
The die filer conjures up images of oldtime toolmakers in white aprons, sitting on shop stools, profiling or putting relief angles on dies. Quiet work by patient oldtimers. It also conjures up visions of doing jobs like making gun action parts on a one-off basis, where filing, trying the fit and filing a little more is often the way. Those are the kinds of jobs I save my die filer and its files for.