As long as the action economy and psi limit allow it, yes
We see on page three of the Mystic class description:
Psionics is a special form of magic use, distinct from spellcasting.
Based on this, it would be inappropriate to use the standard spellcasting rules when using disciplines. Additionally, page 9 states:
The discipline specifies the type of action and
number of psi points it requires. It also details whether you must concentrate on its effects, how many targets it affects, what saving throws it requires, and so on.
As you have noted, nowhere else in the class description mentions a limitation on the number of disciplines that you can cast in a turn, and we shouldn't assume that any rule carries over from regular spellcasting. Based on that, the most specific rules that we have is the standard action economy rules: you can only take 1 action and bonus action per turn, and are limited to 1 reaction a round.
Additionally, Jeremy Crawford has been asked this very question on twitter and he replied:
The rule on casting a spell as a bonus action applies only to spells.
Since Disciplines are not spells, they are not held to the same limitation. As long as you have an action/bonus action/reaction left to use a discipline and the proper number of psi-points, you can continue to use your disciplines as you see fit.
Keep in mind your psi-limit though
The mystic does have the limitation that:
There is a limit on the number of psi points you can spend to activate a psionic discipline.
The limit is based on your
mystic level, as shown in the Psi Limit column of
the Mystic table. For example, as a 3rd-level mystic,
you can spend no more than 3 psi points on a
discipline each time you use it, no matter how
many psi points you have
This doesn't prevent you from using multiple different disciplines in one turn, but it does limit the way that you can use your disciplines in a manner similar to the spell slot levels that a typical spellcaster has.
Have the developers said why disciplines aren't restricted like spells?
Sort of. Often, as with the Kensai Monk, the Unearthed Arcana material intentionally experiments with unusual features, for example not immediately making Kensai Weapons also Monk Weapons. They could be performing a similar experiment here. The spirit of this material is that the DM will make a call regarding ambiguity in the class, and then the surveys will inform the team about how people are playing the class. Or as JC put it here:
The mystic is an example of us testing a concept in UA: is it fun to represent a different mode of magic with a different subsystem?
Based on this, I would say that their decision not to have the mystic follow the same rules is intentional.