That is not the case.
A good B2B will have a constant current all the time the
battery is in Bulk mode (this is why it is also referred to as Constant Current mode).
And as the voltage continues to rise in that mode while the Current is constant, the B2B output is increasing as the voltage rises (P=I*V)
I'll throw in some graphs I did from my own testing, to show this is not some theroretical copy and paste from "the internet", but actual real data ....
Battery Bank is Lead Acid AGM, with capacity of 380Ah@C20, taken down to 50% DoD prior to testing start. B2B is an Ablemail AMC12-30-30E, configured for Std Lead Acid Technology,
Orange Line is Current; Blue Line is Voltage

BT - Ablemail V_C by
David, on Flickr
You see that for four straight hours the Ablemail Charger is outputing at maximum current (actually more. It is officially rated at 30A, but will put out slightly more) whilst the voltage is ramping up as the
battery is getting charged.
It is only when the voltage has plateaued that the current starts to reduce (and the
battery has moved from Constant Current to Constant Voltage aka Absorption mode).
After a couple more hours, the B2B goes into Float Mode (that is a programmed feature within the Ablemail B2B in fact after a set period of running, as it is not expected someone drives non-stop for over 6 hours)
The same timeline showing the Power (watts) drawn by the B2B shows it is slightly increasing all the time as the output Voltage increases whilst the Current stays constant

BT - Ablemail Watts by
David, on Flickr
(P=I*V ==>I is constant, V increases therefore P increases)
You can expect the same behaviour from any good B2B Charger. The Ablemail unit is exceptionally good as you can see from the quality of the current output. The
Victron 30A Smart-Tr B2B exhibits the same kind of behaviour.
The Redarc 40A B2B unit I evaluated was pretty good as well but did have occasional glitches over the time scale which was a little disappointing, but still reasonable enough.
The above data is why I only directly recommend/supply/fit Ablemail or
Victron B2Bs as I know from experience they deliver what they promise.
If you have a B2B where the current is always lowering as the voltage increases, then that basically is probably not a good B2B. If the output suddently lowers after a period, then it is probably the B2B dropping to a lower setting as it overheats. Again, not that great.
If the output fluctuates then that could be just a consequence of the Alternator output varying as engine speeds change, but once got started on a drive, unless it is very stop-start, the B2B maximum - especially at the smaller (sub 40A versions) - will be less than the current the Alternator is putting out so that should not be a limiting factor so the B2B fitted may play a part in this as well.