There's no set rule but responsible breeders will always work with a family -- when you see websites that just list the puppies and show various shots of their markings so you can pick one out that way, beware. Some breeders always match the puppy with the best personality for the particular people interested in a puppy, where others have people over and the people select a puppy in a litter.
I think for responsible breeders it is always at
least a mix of the two -- speaking from my experience of running a breed rescue for cavaliers, I certainly do not just home any adult dog to any family as some would definitely not be suitable and vice versa, so why a breeder would home any puppy to any family, without offering advice and getting to know the family's interests and desires, is beyond me. I can easily say that a significant portuion of the dogs that are given in to pounds, and to me directly in rescue, come in because the wrong personality of puppy went to the wrong people. Most often this is clearly the result of people following that old (and IMHO dangerous) chestnut that the puppy will 'pick' you out when you arrive to see the litter and the first puppy that comes to you must be the one to take. Well, the first puppy is simply the most outgoing in the litter, which is great if you want a highly active and outgoing adult that is also likely to be the most demanding and most at risk of behaviour and training problems in the wrong family. This is just the type of dog I most often get into rescue when the reason for handing over the dog is 'it is too much for us'.
On the broader picture -- labs are I believe the single most popular breed in the US still, and there are a huge number of registered breeders (much less the BYBs and puppy mill labs). If someone wants a lab, it is fairly easy to find breeders and available litters and they have large litters too.
Cavaliers on the other hand are still a fairly rare breed in the US, especially beyond the two coasts, and most reputable breeders do have waiting lists and the dogs have small litters -- a singleton puppy is not that unusual but generally only 3-5 puppies, and many breeders will be some physical distance from the buyer, who may need to fly out to collect the puppy and meet the breeder as well at some point, so it is a lot less likely that buyers can visit and see a whole litter of available puppies and pick out any particular puppy -- any buyer should be very cautious when this is the case as to why the breeder has so many puppies available.. .
I know that the next time I get a puppy (not in the near term! :lol
I will ask for the most outgoing puppy as I want a dog suitable for an active lifestyle, agility etc. I know from experience this is definitely a more difficult dog (going by my Jaspar! :lol
but also the type of personality I like best and I want the breeder to pick the most appropriate personality -- cosmetic issues like markings I don't care about as long as the puppy is from a health focused, conformation focused breeder. Such a dog is totally wrong for someone wanting a quiet low key dog or a casual companion for relaxed walks and lounging around the house -- and that is why those dogs tend to be the ones I regularly see in rescue, as many people do not really want this type of adult.