It's too bad that Grimm Stalker isn't around: the true champion of not using doctrines.
If you want to know how doctrineless armies look, you can take mine as an example. I haven't used a doctrine yet, and I don't know if I ever will.
I was told early on in my guard career, far before I had started actually playing that it was best to start a guard army without doctrines. The idea is that it is important to gain experience with what a guard army is supposed to do, rather than what you think it's supposed to do. Then, afterwards, so the rationale went, if you want to then change the way that your army fights (now that you've already understood what it's strengths, weaknesses, and play style are), you can then add doctrines to tweak it in interesting ways. Otherwise, it was said, you would lose a lot of games by throwing around a lot of points on doctrines, and trying to play a guard army in ways that is simply was never meant to be played.
Anyways, I took that advice to heart, and when I started playing, I started without doctrines. Personally, I think it was a good idea. I didn't get stuck with the impression that guard are supposed to be static which comes from doctrines like cameloline, and I didn't get stuck with the impression that guardsmen were better than they were supposed to be with doctrines like carapace or sharpshooters. Most importantly, I didn't start the bad habit of paying too much for guardsmen, freeing up the points for my one true love: firepower.
While you do technically get to use all restricted troops, and thus doctrineless systems are more flexible, I've found that I haven't taken enough restricted troops to justify it to the average doctrine loving guardsmen. I do feel like I can experiment a lot more, personally, as I don't have to constantly rework my fluff of the entire Foleran Army every time I want to try out a new unit.
As well, by now it's sort of a matter of principle. If I can be successful without doctrines, I have more credibility if I tell people not to take them. Given that I still think it's better for guard commanders to start without them, and to keep on not using them until they really get at least a basic feel for what different units can do in what combinations, this will probably keep me with a vanilla army for awhile.
That being said...
The main advantage I find with doctines is it allows you to come up with quirky lists
This is what I think that doctrines are good for. Once you've become a guard master, I think it's neat that you can then screw around and try some really weird stuff with a reasonable chance of success. As I already said, for new people, I think it just screws them up, and causes them to lose more than they should.
Anyways, that's just what I think. If you want to play a vanilla list, know that you absolutely can do it, but if not, that's okay too.