Shodan is far from the only 'player' in that space. And the scan's aren't necessarily as noisy as you think.
There's enough 'internet background radiation', script-kiddies and virus's scanning the internet, that a heavier-weight scanner that has a few agents to do the scanning, and is somewhat clever about how they allocate IPs and ports to the agents can disappear into the background noise.
And if you really want to spread out the load, it'd probably be depressingly easy to recreate the 'internet cencus 2012'/ Carna botnet https://en.wikipedia.org/wiki/Carna_botnet
NB that having something like Shodan is invaluable to defenders in identifying potential hosts for botnets.
There's enough 'internet background radiation', script-kiddies and virus's scanning the internet, that a heavier-weight scanner that has a few agents to do the scanning, and is somewhat clever about how they allocate IPs and ports to the agents can disappear into the background noise.
And if you really want to spread out the load, it'd probably be depressingly easy to recreate the 'internet cencus 2012'/ Carna botnet https://en.wikipedia.org/wiki/Carna_botnet
NB that having something like Shodan is invaluable to defenders in identifying potential hosts for botnets.