It almost seems to be an article of faith and this is why I would like to illuminate this controversal issue. There is an enormous number of digital multi-effects: The Strymon Timeline, the Eventide Timefactor, the Empress Echosystem, the Source Audio Nemesis or the Boss DD-500, are the most famous ones. Each of them provides numerous types of delays and can be edited in different parameters.
Is more always better?
Surely, the modern digital delays are pretty comfortable. Having tap tempo including subdivisions, modulation, midi control and stereo in- and outputs. On top you will get copious additional features like an included looper or a reverse echo with pitch effect.
For a guitarist of a top 40 coverband who needs uncountable different sound for one show a digital delays might be the perfect choice.
Although these multi delays are bigger than conventional pedals but in the end they need less space on the pedalboard than two analog and digital delays, not to mention a real tape delay.
But are these multis able to reach the sound quality of a single delay? Although the development is far advanced I would deny this question.
Digital delays in fact offer a great number of parameters to adjust the sound but I think that it is impossible to emulate the sound of a Boss DM-2 or a Deluxe Memory Man exactly.
Indeed some digital emulations enable the user to set the proportion of hiss (of an analog delay) nevertheless it is impossible to control the frequency response in such a way to emulate the natural sound variation of the repeats of an analog delay. These variations are much too complex and finally you will get a similar sound that maybe is not better or worth but at least is not identical to the sound of an analog delay.
Doubtless the question arises if you will hear the difference on stage or in the audience like you have heard while you have been adjusting the parameters at home. I think this is a question of feeling: when you like the sound you will feel comfortabe and accordingly your guitarplay will be. And this is what the audience will feel.
If you are searching for a specific delay sound it makes sense to chose a single delay pedal. But if you are looking for a wide range of sounds and some inspiring additional features the multi delay might be your first choice.