Many say that deleting the first D-Mail from the Echelon database is what saves everyone, as it prevents SERN from finding out that Okabe and the others are experimenting with the Phonewave and other technologies.
However, in the timeline where this happens, the Time Leap Machine is already finished. To create the Time Leap Machine, Daru needs to use SERN's LHC, and in turn,
to use the LHC, there has to be a direct connection between the lab and SERN.
It's assumed that for that connection to exist, SERN would have already detected Daru's hack by then.
My question is, if SERN already detected the hack and the direct connection to use the LHC, why does deleting the first D-Mail change anything?
Even if the D-Mail disappears from the database, the record of Daru's hack and the unauthorized use of the LHC should still be there. Isn't that hack enough for SERN to find and capture them? Why does the convergence of the Alpha line depend strictly on that text message and not on the fact that they hacked a global organization to use its particle accelerator?