ADCs for sensor arrays
Most of the ADCs I see are designed for a single sensor voltage.


Hm, well, that depends on where you look, and what you look at. So I'd say that presumption is wrong, in general.


  are there multichannel ADCs that accept 100 or 1000 analog inputs and have an advantage over multiplexing? If so, what is that advantage?


There certainly are systems that have a whole lot of coherent ADC channels – not necessarily inside the same silicon chip, but distributed across multiple synchroniced ADC ICs.

Very simply because your assumption "My single channel is much narrower than what technically feasible ADCs can do" breaks down for other channels. 

Assume you're doing digital beamforming with 128 channels of 40 MHz each – typical 5G research. Where's your single ADC that can cover that bandwidth by multiplexing now?

The fact that ADCs exist that have a far higher bandwidth than your signal is not because someone wanted to do hundreds of your signals at once, but because they needed to capture a wider signal. For that wider signal, at the time the ADC that could cover that was developed, there inherently existed no ADC that could do multiples of them. So, your question seems to be a little too focussed on your own problem, ignoring other signals that exist.


  So, for example, if you want to sample at 10 kHz, which is sufficient for underwater situations, and you have a 100 element array, then you would just need for the ADC to be able to sample at 10 kHz * 100 = 1 MHz which an ADC can do no problem.


Well, add in the fact that a switchover takes time, too, so you'll have additional signal distortions, as well.

Notice that if your switching frequency  is \$f_M\$, your signal will invariantly need to contain a component at that frequency, three times that, five, seven, nine times..., because what you're effectively doing is taking $N$ signals \$s_n\$, and multiplying each with a periodic rectangular signal \$r(t)\$ of \$\frac1{f_M}\$ width, shifted by their individual position in the multiplex sequence. So what you get as sum signal going to the ADC is

$$
s_\Sigma(t) = \sum\limits_{n=0}^{N-1}{s_n(t) \cdot r\left(t-\frac n{f_M}\right)}
$$

which in frequency domain becomes

$$
S_\Sigma(f) = \sum\limits_{n=0}^{N-1}{S_n(f) * \left(R(f)\cdot e^{j2\pi\frac 2{f_M} f}\right)}
$$

(\$*\$ is the convolution operator)

\$R(f) = \mathcal F\left\{r(t)\right\}(f)\$ is known – it's a comb of diracs with descending amplitude, at every odd multiple of \$f_M\$, and convolution with a comb of diracs leads to spectral repetitions. 

Luckily, we defined the bandwidth of the input signals \$b_{in}\ll f_M\$, so that these repetitions don't alias into each other, but it means that your system needs to look like

input signals –> filter to \$b_{in}\$ –> multiplex at rate \$f_M\$ –> filter \$\ge f_M + b_{in}\$ -> ADC

The question of how fast your ADC needs to be is hence answered by how steep your filter will cut off after the minimum it needs to pass; it's usually easier to just make your ADC a bit faster and not use an overly complex analog filter. The first repetition happens at \$3f_M\$, and so you effectively have nearly \$2f_M\$ of maximum transition band (due to switching imperfection, you'd want to stay significantly below that).