- Temperature
- Amount of a substance
- Luminous intensity
are pretty much bogus fundamental units. The unit temperature is just an expression of the Boltzmann constant (or you could say the converse, that the Boltzmann constant is not fundamental as it is merely an expression of the anthropocentric and arbitrary unit temperature).
The unit energy will be whatever is the unit of force times the unit of length. AJoule is the same as a Newton-Meter, which are already defined in the SI system.
You should read the NIST page on units to get the low-down on it.
In my opinion, electric charge is a more fundamental physical quantity than electric current, but NIST (or more accurately, BIPM) defined the unit current first and then, using the unit current and unit time, they defined the unit charge. I would have sorta defined charge first and then current.
Just like the unit charge (or current) is just another way to express the vacuum permittivity or, alternatively the Coulomb constant and the unit temperature is just another way to express the Boltzmann constant, the unit time, unit length, and unit mass, all three taken together could be just another way to express the speed of light, the Planck constant, and the gravitational constant. But because $G$ is not easy to measure (given independent units of measure) and can never be measured as accurately as we can measure the frequency of "radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom", we will never have $G$ as a defined constant as we do for $c$ and as we will soon for $\hbar$ and perhaps for $\epsilon_0$ and $k_\text{B}$.
But once we define length, time, and mass independently, we cannot define energy independently. The Joule is a "derived unit".
EDIT: so i will try to explain why the candela is bogus. (i had already for the mol.) so there is a sorta arbitrary specification of frequency, then what is the difference between 1 Candela and $\frac{4 \pi}{683} \approx$ 0.0184 watts? bogus base unit.
Disclaimer: due to limited connectivity from where I'm now, I can give only a short answer and I'm not able to access useful references.
With the new SI the distinction between base and derived quantities (and units) will lose a lot of its foundational value, and will be kept mostly for historical continuity, and thus, as far as I know, there is no plan to change the set of base units (which would have to be anyway 7, to avoid changing the relationships between the physical quantities) or to get rid of them.
For what concerns the realization (not implementation) of the ampere with single electron transistors (SET), notice that at present the level of accuracy of such realizations is much worse than that achievable through the other path (Josephson effect plus quantum Hall effect), and it's insufficient for primary metrology. In fact, at present, the so called quantum metrological triangle has not yet been closed with the highest level of accuracy.
Best Answer
The radian (not the degree) is the SI unit of angle, and it's defined in terms of lengths: it is that angle for which the length of a circular arc subtending that angle is equal to the radius of the circle. Since this definition refers to the relative ratio of two lengths, the SI considers it to be a "dimensionless derived unit", rather than a base unit.1
As far as bytes go: Defining a unit amounts to specifying a certain amount of a quantity that we call "one unit". Physical quantities such as mass, length, time, etc., are (effectively) continuous quantities, and so there is no "natural" unit for us to use. We therefore have to make an arbitrary choice about how much of each quantity is equal to one unit.
Digital information, on the other hand, is inherently discrete. All methods of quantifying data simply amount to counting bits; and you don't need to make an arbitrary choice of unit if you can simply count a quantity. There is therefore no need to define a unit for digital information, because there is already a natural unit (the bit).
It's important to note that not every measurable quantity is inherently definable in terms of SI base units. If I count the number of people in my office building right now, and tell you that there are "12 people" in the building right now, then "people" is not expressible in terms of meters, kilograms, and seconds. But I don't need to worry that you're going to come along and use some different unit to count the people in this building, because a natural unit (1 person) exists. It's only when we are measuring a quantity that can take on any real-numbered value (e.g., the mass of all the people in this building) that it becomes important to define a unit; otherwise, you and I have no basis for comparison. Any system of units is essentially a set of these arbitrary choices; "natural" units of quantities that are inherently discrete are unnecessary simply because they're understood to be the obvious choice.
1 It's worth noting that the radian was officially a "supplementary unit" in SI until 1995, when they were reclassified as "dimensionless derived units". A bit of the discussion surrounding this change can be found on p. 210 of the Proceedings of the 20th Conférence Générale des Poids et Mesures (warning: large PDF). Reading between the lines, I suspect that the name "dimensionless derived unit" was something of a compromise between those who thought it should be thought of as a derived unit and those who didn't think it should be thought of as a unit at all; but I wouldn't want to speculate further than that.