Occasionally someone “opens” an investigation but it seems no one just “starts” one.
I think launching comes from the late Latin «lanceāre», meaning throwing a spear. Investigators like bellicistic expressions, makes them look resolute and powerful. Guarantees success!
Open an investigation is the bureaucratic version: you open a file like a book on a desk, lick your pencil and start writing the results. Much boringer.
Is it any more than imagery? Launch suggests something complex done under orders from important people.
We sometime file complaints but, when we really mean them, we lodge a complaint.
Congressional investigations on C-SPAN don’t seem launched - just unmoored.
To me, “Launch” implies there is a reasonable chance it might fail.
FWIW: The first cites I came across in a quick search regarding “launch” and “investigation” were from 1907, so we’ve been doing it a while.
We also launch new programs, experiments, campaigns, businesses, servers, websites, video games, lawsuits, careers, missions, expeditions, rants, products, revolutions, rockets…
Seems like it’s just a generic verb to powerfully start something?
Or that marketers wrote the press release 
It’s an analogy to a ship setting out on a voyage. Back in the day, when you thought of big and powerful things starting to move, you thought ships. It would have been an obvious comparison.
The analogy may be there, but the
Etymology (from wikidictionary)
From Middle English launchen (“to throw as a lance”), Old French lanchier, another form (Old Northern French/Norman variant, compare Jèrriais lanchi) of lancier, French lancer, from lance.
still comes from a spear or, if you prefer, a lance. When you launch something, you throw it like a spear.
In etymology, we end up throwing things a lot - “parable” goes back to a word meaning “to throw down alongside” (as you would to make a comparison between two things) - and it’s cognate to words like “parabola” and “parallel”).
Papa does…
♫ The mama pajama rolled out of bed
And she ran to the police station
When the papa found out he, began to shout
And he started the investigation ♫
A lovely bit of Simon nonsense!