Actually, it's worse, by orders of magnitude, not just not really that useful, even as a control channel. You can't just transmit VFT over a 3kHz channel width, the actual bandwidth at VLF is measured in Hertz or milliHertz, not kiloHertz. This in no way corresponds with the baseband frequencies of analogue telephone line comms systems, which is where the 300 baud assumptions are comings from. It's far, far worse than you imagine, making it impractical to use as a control system. It reduces the practicality to "on or off", which is effectively pointless, as optical losses are measured continuously.
300 baud is do-able data rate for FEC transmissions in the HF and MF regions of the spectrum, even at LF. At these frequencies, the bandwidth of the antenna and associated matching system are high enough not to impact on the bandwidth of the channel.
A radio transmitter with a wide bandwidth (as a percentage of the centre frequency) is so difficult to match that losses become untennable at even a few tens of herts from then centre frequency. This restricts the bandwidth of the channel (and hence the available shifts and data rates, even in the post-Shannon era, to very low rates indeed.
Radiating a good 7kHz-wide voice signal at 150kHz is difficult, but consider that it's 2.4~ish% of the centre frequency. This example is the bottom of the "LongWave" broadcast spectrum. It's also comparable to some Loran and similar navigation services. Even that produces severe matching problems (trading bandwidth for Q, as Q decreases, bandwidth increases but so do the losses in the amplifier>antenna matching network.
Now, make that 1.5 kHz, the middle of the ULF spectrum, taken as a purely mathematical example. Instead of 150 kHz and you have the same %-age off the centre frequency at only 700Hz from the centre frequency. It's this that limits the effective usable spectral bandwidth of the system, generating the signal isn't so much a a problem, but coupling it to an antenna is, given that the antenna efficiency itself will also be extremely low, due to the long wavelength at ULF. it's doesn't take long before several different power losses of 30dB add up to give you massive power loss. Try minimising antenna losses that by reducing resistive losses and ground losses (requiring massive ground mats and extremely long radial systems. Then you have to increase transmitter power to compensate the matching losses. Before long you're looking at 50kV insulators and several kiloamps of antenna current as you try to trade Q against bandwidth against losses against costs. There's a reason morse was used in the marine MF band and not voice - around 500kHz or lower and matching become a very serious business, so mobile transmitters become problematic in terms of wider matching, given the limited transmitter power available. At higher frequencies, noise (both natural and manmade) was more of a reason to limit signal bandwidth (usually in the receiver system, using high-Q filters, often piezo-quartz filters in superhet designs. These were in the days preceeding DSP weak-signal methods that have revolutionised radio systems in the last 25 years. The antenna matching was far easier due to the manageable antenna proportions at high-MF and HF.
Reducing the spectral utilisation helps immensely, giving a practical (for a superpower defense budget) throughput of single-figure of baud.
For the old US and Russian systems, 76 and 82 Hz respectively using chunks of the planet as the antenna systems (yes, the planet), the problems increase by magnitudes again, making them Extremely Low Fart-rate systems
It's far easier to tap at a friendly landing station; failing that tap undersea. Such "intervention" as these subsea jobs are called is far from impossible, as others have noted. Whether it's worthwhile or not given the expense is another matter. Live-working on 10kV DC systems is not impossible using isolated ROV and robotic systems - I've personally seen it done (on a CCTV feed!) on oilfield jobs at 600Vdc+ with minimal problems other than pumping the environment dry and using live-working tools and equipment. and that was using human divers, albeit carefully. These jobs are not done by choice, only by necessity, but are nonetheless doable in relative safely for the operators concerned.
source : I used to design, tune and match VLF systems. I then spent several years on subsea comms: wideband, voiceband and narrowband, using Hertzian, acoustic and tug-on-a-rope methods.