Let us dispose of the term "point-and-shoot" for a moment, and replace it with "fixed-lens". "Point-and-shoot" implies a mass-market snapshot camera, and the class of fixed-lens cameras goes well beyond the mass market into the realm of cameras that would easily wipe the floor with any entry-level DSLR or MILC in their specific use case. But when you get to that level, fixed-lens cameras become very specialized, very expensive, or both.
The Sigma DPx Merrils, for instance, will give you utterly breathtaking image quality at low ISOs, but the cost a thousand dollars apiece, can't really be used above ISO 400 at all, and you need a whole different camera to change focal length. The Fuji X100s is a street-shooter's dream come true, but it's rather expensive and has a single fixed focal length. The Sony RX1 is a full-frame camera you can put in your pocket, but again costly and a fixed focal length.
You can get a good compromise between IQ, large-enough sensor, relatively good, fast glass and a large zoom range in a fixed-lens camera (at least one, anyway: the Sony RX10), but you are kissing the entry-level DSLR price range a fond farewell and are stepping up into what can only be described as "enthusiast" territory. (And if you want a prestige brand, Leica and Hasselblad will gladly sell you rebranded versions of other cameras at a huge markup.) Other high-IQ fixed-lens cameras tend to have zoom ranges not significantly different from the entry-level DSLR/MILC kits.
The entry-level DLSR or MILC will give you more for less, at the penalty of having to buy a two-lens kit (or an additional lens to go with the standard kit). Yes, the system will be bulkier and have more to fumble with to go from wide-angle to long tele, but there is, in compensation:
Of those, the "considerable cost savings" is probably most important to present you. You really have no idea what future you may or may not want, and paying more right now for something you might find completely unsuitable in the near future makes little sense (especially since fixed-lens cameras don't hold much in the way of resale value). If you were experienced enough to say with certainty that a particular fixed-lens camera will completely cover your needs, you might be able to justify spending the extra to get the convenience. But as a beginner, you'd be locking yourself into a range of photography that you cannot step out of unless you buy another camera.
That is not to say that there's no value in having something like a small-sensor superzoom/ultrazoom/bridge camera. If you don't particularly need shallow depth of field except in "macro" shots, don't expect to work in low light and don't foresee using you images for anything other than screen presentation at reduced sizes or small (8x10 or smaller) prints, there are plenty of cameras out there that fill that niche, each of them more-or-less equivalent to the others, but with minor feature differences. For some value of "good enough", they really are good enough; you just need to know what "good enough" means to you, and it is very hard for a beginner to know that. It may be the best $500 you ever spent, or it may be $500 down the tubes.