Because it doesn't work that way.
To start with, $f(a)$ is not a point. It's only a number.
An example of a point on the graph of $f$ is $(a, f(a))$--two coordinates, $a$ and $f(a),$ to plot a point in the plane.
Next, $f'(a)$ is the slope of the tangent line. You may have realized that already, but remember that the equation of a line in the $x,y$ plane
satisfies $y = b + mx$ if and only if $m$ is the slope and $b$ is the
$y$-intercept of the line.
So if we can figure out a number $b$ such that the tangent line at
$(a, f(a))$ goes through the point $(0,b),$ then we can write
$y = b + (f'(a))x.$
There is a more generally-applicable form of the equation of (almost) any line in the plane, which lets you write the equation for a line easily once you know its slope and any point that it passes through (not necessarily where it intersects the $y$ axis).
For a line with slope $m$ passing through the point $(x_1,y_1),$
the equation is
y = y_1 + m(x - x_1). \tag1
The equation can also be written in a slightly more symmetric form,
y - y_1 = m(x - x_1),
which tells us this is the equation of the line we get if we translate
the line $y=mx$ upward $y_1$ units and $x_1$ units to the right
so that it goes through the point $(x_1,y_1).$
For the tangent line, instead of an arbitrary point named $(x_1,y_1)$ we have one named $(a,f(a)),$ and instead of an arbitrary slope $m$ we have slope $f'(a).$
So where do these new symbols fit into Equation $1,$ and what does it
look like after we update it to describe the tangent line?
Of course you still can write an equation for the tangent line
in intercept-slope form if you really want to.
Just observe that the equation of the tangent line says
$$ y = f(a)+f'(a)(x-a) = \left( f(a) - af'(a) \right) + (f'(a))x, $$
so the $y$-intercept of the tangent line is $f(a) - af'(a).$