Some people are staking out some narrow positions here
I usually carry a small folder (spyderco delica) when running. Clipped to waist band or in jacket pocket (if it is cold enough to wear a jacket). It is hardly noticeable.
The things I look for in a knife to carry when running are:
- light weight. Heavy knives are just not conducive to running.
- able to carry comfortably (pocket or waistband) - should not bang against me (so no neck carry) or pull my pants down

- big "enough" for likely needs (cutting rope, building an emergency shelter, defense against wildlife - 2 leg or 4 leg). Knives serve a lot of purposes, some more likely than others. Any choice is a compromise (not ideal for all or even any single purpose), but why carry something that is just inadequate for anything ? Just an fyi - a 3" blade is always going to be minimal for purposes of self-defense, but it is only a tool to facilitate defense, not the only part of your tactics, and don't forget - flesh is compressible. If I punch a 3" blade into a soft body, it can penetrate more than 3". I would not want to bet my life on it against a grizz, but then for a grizz I want at least a 45-70 and not a knife at all. But dog-sized animals, cougars, etc, it is definitely better than nothing.
The advantages of a folder (all else equal) are compact size when folded and "sheath" is built in.
The disadvantages are deployment and strength. Deployment can be particularly an issue in winter with gloves on.
A fixed blade (all else equal) is less compact (does not fold), and needs a sheath, but is faster, easier to deploy and stronger for hard cutting jobs.
The Izula is very light and very similar in size to a lot of small folders, is comfortable for pocket or IWB carry, and at least as capable a cutting tool as a small folder (ok the blade is a bit thick, but not overly so).
Carry whatever you want, or not at all, but I don't see much of a downside to carrying an Izula versus a small folder, and there are some advantages. If small folder or fixed blade is too small for you, carry something bigger ! But I don't unless I'm wearing a pack (which I often do when running in winter - for survival gear).
I run "trails" in "remote" areas, btw. In the dark (after work - it gets dark early up north). Last night the temp dropped from 25F to 15F during my 1 hr run. We just got a little snow too, and if the wind had kicked up, I could have been several miles from home, in a blizzard. Probably being stalked by mtn lions
