I was making a companion, a spanish friar, when I noticed something odd. Grogs are not allowed to take story flaws. Monastic Vows are story flaws, and major ones at that. Therefore, all deeply religious people are companion-level characters, True Faith or not. Weird.
Grogs are "red shirts." Maybe that doesn't carry any meaning anymore with today's youth, but grogs are meant to be scenery, spring traps, die dramatically, be comic relief, etc. Grogs are not meant to drive stories. If someone is important enough to have a story revolve around him or her, then that character should be a companion.
Imagine a Monk, Friar, Priest, or Nun leaves his or her religious duties, organization, etc. to go hang out with a bunch of godless, heathen wizards, and the local religious authority finds out. That's a pretty major story that's going to bring some religious interference on the covenant. In general, a grog shouldn't have that kind of power to affect the entire covenant.
Story Flaws that never have stories based on them aren't flaws, grogs can't drive stories, therefore grogs can't have story flaws. That's the metagame reasoning, you're of course free to do whatever you want in your own game.
And by that measure your obvious solution is to just not give the grog the flaw. They'd still have the vow you just wouldn't wrap stories around it.
What's the difference between a grog and a companion who only took three points of flaws and matching virtues? Only spotlight time.
I imagine anyone can take monastic vows, but not the Monastic Vows Flaw. Only companion-level characters can be developed enough to be able to play Story Flaws, because grogs are less important characters by definition.
That was what struck me as odd, Eric D, because it states that a Mendicant Friar MUST have the Monastic Vows flaw. Just an oddity. I'm not really inclined to worry about it.
And, fortunately, I was born in the redshirt years and grew up on watching them be disintegrated by any manner of things. =)
I wouldn't say that's the only solution. If you want to have a Friar in your covenant, make him a companion. Easy solution. In the last game I played, the alpha storyguide had multiple companions and no magus, it worked fine. We had a player with a magus who was a serious lab rat, he had two companions and no grogs. Nobody had any problem with it.
But to your second point, spolight time is the main difference between a grog and a companion. Grogs are meant to be minor characters. If you're running a covenant and someone with a Major Story Flaw applies for the shield grog position, are you going to take him? Why allow the covenant to be drawn into this character's drama when the only service he's providing is as a spear blocker. Shield grogs are a pfenning a dozen. Now if he's a companion and has a boat load of great skills to assist the convenant, then maybe he's worth keeping.
I'm actually having a similar issue in the game we're playing. I have a companion, Eldragil, a half-sidhe knight whose attitude is much that of a cat. He's fun in a creepy way, not at all nice, and believes the world is here for his amusement. He's really a rather scary individual.
Then there's his herald, Hector Belatortuga. Hector is a bit like the Jeff Chaucer character from Knight's Tale, an outrageous herald, wild storyteller, semi-competent warrior, and wears a magical tortoise shell on his head that he believes will allow no harm to come to him. He speaks like a wound up Antonio Banderas and is probably the most fun I've had playing a character.
The trick is he feels more like a companion than the grog he is. He's the single most consistently played character in our little Saga, goes out with the group as often as his schedule allows, and is just a riot to play. He's just so loony that he steals the limelight from the other, more game-important characters.
Isn't that the point of a Grog? ...Have fun playing them, but don't worry if they get killed????
Our favorite grog was recently 'demoted'...we were all kinda bummed..but hey, we have another 150 or so in the pile...
I've got a Shield Grog, Hirohito. Built under 2nd edition rules he has one virtue and one flaw. The guy just never died. Though he's retired now, at his peak in 4th edition, he casually went on companion adventures. Through the various editions I was given permission by the troupe to rebuild him as a companion, but I kept explaining, "Then he wouldn't be a grog!"
I love Hirohito, he's 'the grog that lived!" 
Some characters just deserve a little more.
Our grog Niccolo recently received an upgrade to Companion status. Our steward, Fabian, will probably have the same as he turned out to be pretty central in a recent murder-mystery story.
Don't be afraid to do that to reflect the troupe's opinion.