I've had a number of people inquire about apprenticeships over the last 20 years, but it's a pretty rare request. I honestly believe that the age of apprenticeship has passed, for the most part.
The internet plays a part, because information of all kinds is so easy to access. Fifty years ago if you wanted to learn how to be a flute maker you had to find a flute maker to teach you, or you had to be extremely motivated and good at reverse engineering

I started making flutes in 1997, so it was post-internet but pre-YouTube. There was some information online, but it was not anything as plentiful as today. So I ended up teaching myself. I scraped together whatever bits of technical info I could find and then just did a lot of trial and error. I reinvented the wheel a LOT along the way but I didn't know how else to proceed.
Personally I find the notion of trying to train someone rather daunting on a couple of levels. It's time consuming, first of all. I had a friend spend a day in my shop at one point, and I was going to teach him how to operate my gun drilling rig so that he might possibly work for me on occasion. It was an eye opener! When you do something every day for years it is easy to loose touch with "beginner's mind" and trying to convey skills that have been acquired over years--many of them intuitive--is surprisingly tricky. It didn't work out.
And then there is the economic aspect. Teaching is time consuming and involves giving away hard-won knowledge. What is the benefit to the flute maker? Unless the apprentice is either paying the flute maker some sort of tuition, or agreeing to work for free for a number of years, there is not much motivation for the artisan to take the trouble. Some makers, such as Terry McGee, are also preservationists of flute making knowledge. Terry is always willing to help (he assisted me very generously when I started making Irish flutes) and he has spent years making his website into an amazing resource for others to enjoy but he is really the exception and not the rule. I don't mind pointing new makers in the right direction in the same way that Terry does, but I've had a startling number of inquirers write to me blatantly asking me to simply e-mail them all of my shop notes, measurements, etc. so that they could make (and sometimes sell) their own flutes. That always leaves me nonplussed. I've spent thousands of hours figuring this stuff out and then someone who clearly wants instant gratification actually asks me to give it all away for free so that they don't have to do the hard work.
Therein lies the difficulty with an apprentice. In days of old, the apprentice spent years with the artisan, exchanging useful labor for knowledge before striking out on their own. How would that work in the modern age? An artisan might spend valuable time teaching an apprentice, who then moves next door and hangs their shingle. It's a dilemma. I think that passing on knowledge is important, but making a living is also a reality. I work alone and teaching would be a massive time-suck with questionable economic benefits, unless I also had a son or daughter who was interested in the business. If there were some sort of contract between the artisan and apprentice it might solve the dilemma, but it's going to be a rare individual who would be willing to actually undertake being an apprentice on terms that were also useful to the artisan.