as a healthcare provider, I'm curious as to the benefits, nutritionally, of breast feeding for so long.
It depends entirely on what you mean by "for so long."
My DD was getting 90% of her nutrition from breastmilk when she turned 1; multiple food allergies plus her willingness to go hungry rather than eat significant amounts of solids (not unusual in kids with multiple food allergies) meant it was breastmilk or nothing. So for her, she got lots of nutritional benefits at that age.
When she was 2.5, I weaned her cold turkey for 2 days, because I just could not stand it for one more moment. Despite Sudafed and cabbage leaves, I was sooooo sore and sooo miserable and sooo engorged. Way more than I ever was when she was a newborn. So I suspect she was getting a substantial amount of breastmilk up to that point, too. I figured weaning her might also improve her nothing diet, but it didn't - she's just not a big eater. Since she was still off the bottom of the weight-for-height charts (although her food allergies had been outgrown and replaced by environmental allergies), breastfeeding at that point was probably the equivalent of giving her an Ensure - a little nutrient boost for a kid who otherwise wouldn't get quite enough. Except that, having read the label of an Ensure bottle, I'd much rather my kid have a natural food designed to be ideal for human nutrition.
We compromised on much more restricted nursing (first with chips she could turn in for a "side;" now she's on the "once a day at bedtime only" plan), and the little bugger is still nursing, having turned 4 at the end of May. AFAICT, what's causing her to finally give it up (this week she voluntarily skipped her bedtime nursing for nearly the first time ever, and she's only nursed once in the last 4-5 days) is the complete disappearance of my milk supply.
I personally don't think she's getting any nutritional benefit at all from it at this point. But she doesn't get any nutritional benefit from bedtime stories or scaring away the monster under the bed or holding her hand at the dentist or doing her laundry or any of the million other things that at some point she won't need me to do for her. Up until now, it's been really important to her, and if there's something important and nonharmful to her, essentially neutral to me, and irrelevant to anyone else, it's hard to think of any logical reason to arbitrarily deny it to her. There are enough things that a 4yo is denied or discouraged from for good reasons.
Personally, I don't think it's likely to be relevant whether you as a healthcare provider have any knowledge about extended breastfeeding. By the time you get to a year, you've already got a pretty good idea of how much more you're up for. No amount of "EBF is great!" propaganda is going to change your mind. And your kid has a pretty good idea of how much more she's up for. No amount of encouragement will get a kid to nurse if they don't want to. You can lead a kid to the nipple, but you can't make them latch on.
And if you were overtly negative, I'd either leave the practice outright or just assume that you were the kind of provder who'd rather make things up than say you didn't know and take all your advice with a giant grain of salt, depending on what my other healthcare options were. IMHO, "Whatever works for you," is a fine position to take.
if my children had been born years ago, they wouldn't have survivied, because I wouldn't have been able to provide proper nutrition for them.
Wet nurses, or nutritionally unbalanced substitutes. Babies are tough.
I'm sure I'll get a few of those opinions, anyway! 
The doctor was very happy when I explained that I was nursing no matter what. You're right about how you can't give up your favorites for a diet, but when it comes to child you do it.
Sometimes I wish I would of tried to produce more milk, but it was a natural progression over time. My body knew what it was doing. She nursed for 31 months total. 
But it just seemed to fly by! I can't believe it. I'm glad she made the decision, though.
