Formulae like Alimentum and Nutramigen are called hypoallergenic. Although there is milk protein (casein) in the formula it is extensively hydrolyzed -- broken down into extremely small pieces. (Nutramigen comes with a small brochure with pictures of this inside every tin to help explain it, I'm not sure if Alimentum does?) MOST babies with either a milk allergy or milk intolerance (there is a fine line of difference but it doesn't really matter which it is, LO can't have milk either way) can handle these hypoallergenic formulae without any problems. The proteins are broken down small enough that they can digest them fine.
However, when the problem with milk is extreme, and symptoms are not being adequately treated by using one of the hypoallergenic formulae, then babies are put onto what are called elemental formulae. Named elemental because the proteins are broken down into their smallest form, amino acids. Amino acids are the basic elements of a protein, hence the word elemental. Brands include Neocate and Nutramigen AA for instance (there are others). I'm making a broad generalisation here and it is from my own observation not any kind of "proof" (disclaimer!) but it tends to be babies where the milk reaction causes very bad eczema or blood in their stools who seem to be the ones that need go onto Neocate. Babies who suffer from MPI-caused reflux, tummy cramps, mucousy stools or mild eczema seem to do fine on Nutramigen or Alimentum.
I find that statistics on how many babies have such severe problems and need to go onto elemental milk really do vary. My own paed GI told us that it is less than 5 % of babies with MPI that need to move onto the elemental milk - however I am sure this differs by country as the rates of MPI itself differ by country.
I do think that the vast majority of the time, doctors really prefer to trial the hypoallergenic forumula first. It gives you an idea of how severe the reaction or problem is, for one. Second, the hypoallergenic formulae tend to taste VERY VERY bad and it takes a while to get LO to drink them....well, the elemental formulae are a hundred times worse. They are pretty nasty, at least until LO is old enough to drink the toddler versions of them which come flavoured. Trying to get a baby to drink Neocate can be extremely difficult. And, also, they are EXTREMELY expensive.
To give you an idea of the prices in the UK
Regular milk based formula - appx £8 per 900g tin
Nutramigen (hypoallergenic) - £14.06 per 400g tin
Neocate (elemental) -£35.74 per 400g tin
So, pretty pricey, we are fortunate in the UK that hypoallegenic and elemental are both given on prescription which mean they are paid for by the health service and not by parents.
Not sure if this answers most of your questions or not, hope it's at least helped a bit!