Except they may not have 3 positions open -- just one position, but they may be willing to hire a more junior person with the hopes of training them and given them an upward career path. (Unfortunately for the employee, the pay doesn't typically increase as their skill increases).
It really is 3 positions though, it's just that they can only fill one.
Putting an ad out for all three, means better tuned applicants, and leaves the company the ability to make an offer of a different position. From the company's position, that's 1.5-3x the number of applicants, for the price of 2 additional ads.
When our company is looking for mixed positions (either a mid-level position where we'll also accept a junior position, or a mixed role such as dba/sysadmin), we'll put out two ads for the position that focus one aspect, then mention the other as a nice-to-have. Then we get candidates who are strong in one area, and average in another, or sometimes (when we're lucky), someone who is strong in both. But either way, we get to choose the best candidate, rather than having good candidates self-select out due to "you must have everything" or super-vague posts.