Why should Vbb not exceed the barrier potential values?
To my opinion, the quoted wording is rather confusing: "The voltage VBE across the forward-biased junction is very low".

In fact, the user is biasing the B-E path with an externally applied voltage. Hence, it is not "very low" but it depends on the selected biasing network. And this voltage must not be much larger than the mentioned 0.7 volts - unless you are designing a transistor stage with a very large collector current Ic=f(VBE).

Perhaps the author was referring to the internally developped diffusion voltage across the B-E junction. However, in this case, he must not speak about a "forward-biased junction" and he should use the term "diffusion voltage". This voltage acts as a kind of internal "barriere" that must be neutralized (compensated) by the external applied voltage.

Of course, the applied (or generated) voltage VBE is allowed to be somewhat larger than the diffusion voltage. In this case, it is best to remember the well-known Shockley equation: Ic=Is[exp(VBE/Vt) - 1].

(Is: saturation current, Vt: temperature voltage). From this equation it is clear that we have a (small) collector current also for VBE=0.5 volts and a larger one for 0.75...0.8 volts.

Comment: Because of heating effects and other undesired influences it is dangerous - as mentioned by Bimpelrekki in his comment - to use the transistor stage in the shown simple ciruit. Instead, it is necessary to stablize the desired collctor current using negative feedback (emitter resistor).