First off, there is no such thing as a signal with zero bandwidth. That is like the imaginary line between two imaginary points - the line with no width between points of no size.
It is like saying isotropic antenna. (An FCC favorite)
There simply are no such things except as theoretical constructs - end even then, to prevent dividing by zero, they always must be expressed as limits of variables as they approach zero.
CW transmitters always begin at zero output (what you are calling a zero-crossing, but at the boundary condition) until they are commanded to produce a signal by the closure of a contact on a key or by other means. Then they return to zero when that output command is removed.
CW transmitters do not come up to full power instantaneously, and produce waveforms like this:
Note that as this is displayed in the time domain relative to the keying frequency, the actual carrier is not visible.
So even if the modulation itself (the key, acting as a switch) is a square wave, the resulting output is not truly square due to the physical constraints of the components of the transmitter.
This is true for both the rise and fall of the envelope.
Here is another example:
In this plot, relative to the carrier frequency, it is clearly seen that in a practical sense the transmitted wave envelope does indeed begin and end at the boundary conditions of zero.
Of course, philosophers have been known to argue that it never actually reaches zero - just gets closer and closer to it. Then the quantum physicists bring up the Planck limits, and so on, ad nauseaum.
In the frequency domain it will look like this:
Note that this is a plot of a signal modulated by 1 KHz square-waves, which is why the bandwidth is spread so widely. At 1 KHz keying, the ratio of signal to modulation frequencies are getting to the point where it is producing sidebands. The amplitudes of the sidebands fall off in the normal way. This plot does not show the effects of input filtering.
Consider a generic mixer circuit - the output should always be filtered in such a way that only the desired modulated carrier is the resultant output.
The risetime portion is as if it has been modulated at some very high rate. That produces spurious emissions in the driver circuit which are then filtered out. They should not be within the bandpass of the final power amplifier.
But since no filter is perfect some of those spurs will end up on the output. Hence the need for guidelines regarding limitation of spurious emissions. These are specifically regulated for FCC Type-Accepted commercial transmitters.
Ultimately, you want a transmitter that exhibits higher Q as a measure of how well it applies available power to the desired output frequency for higher efficiency.
Here is an interesting article on the subject (slightly TL;DR):
Effect of Keying Waveform on CW Bandwidth
the transfer function of a real transmitter is NOT linear.
i.e., a square-wave input (where the rise and fall time is as if the frequency of modulation is at the boundary condition of the limit of it being at infinity, where the limit of the period of modulation approaches zero.
Bottom line is that since there is no carrier between the Morse elements, the output always begins at zero and ends at zero.
Hand keying is at such a slow rate as compared to the carrier frequency that it is not very relevant.
The O-scope trace at the top is taken from a 630 Meter transmitter, and even then the modulation rate is still so slow compared to even that low of carrier frequency that there are no clear artifacts introduced by keying at random time relative to the carrier oscillations.
It is the modulation frequency that is the dominant factor in producing the final signal bandwidth.
As an aside, back in the day when the FCC had monitoring stations all over, I would visit sometimes and watch as they used what they called "TXID" - Transmitter identification - the way a signal from a CW or FM transmitter wanders in frequency and amplitude as they were keyed up. They were very good at this, and often could tell who was transmitting before any identifying modulation was applied. i.e, saying or keying a callsign.
They told me that even with the same models of transmitters made on the same production line on the same day there would be measurable differences due to the tolerances of the various components that went into the final product. They considered this to be closely-held information at the time.