Here is an extract from the 2N3904 data sheet.
See the graph entitled Base - Emitter On voltage versus Collector current.
This clearly shows that the collector current is controlled by the BE voltage.
It is an expotential function but as the graph has a log scale it is approx straight.
For example, on the 25 C curve, at Vbe = 0.6 Volt, the collector current is 0.1 mA.
At about 0.75 Volt, Ic = 20 mA.
If you study the fundamental operation of transistors, the collector current is controlled by the charge in the B-E region and since Q = CV, the charge is proportional to the BE voltage. So you can say it is voltage controlled.
This is why circuits such as the current mirror work.
There is no doubt that Ic = Beta Ib is very useful, but it does not mean that the Ic is current controlled. The base current is necessary to keep the BE charge constant since some charge carriers in the BE region are gobbled up by recombinations and become a component of the emitter current.