On one hand, I understand that some people think it's about time to move on. On the other, BioWare added some very nice MP content that will never be available again after they shut off the servers. I feel that to be a tremendous waste.
I also know that BioWare are under no obligation to kill off ME3 when Andromeda comes out. They are also under no obligation to keep them up either.
I expect that they would shutter them hamsters shortly after ME:A to focus and promote the new game. I hope I'm wrong. I love hamsters. 
Anyone who wants to move on is free to do so, just as anybody who wants to keep on playing an old favorite game shouldn't have to be harassed or criticized for it.
As to the idea that a game's servers are likely to be shut down when the sequel is released, please provide me with examples. I haven't been able to find any myself. What I seem to find is that servers are typically shut down several releases later. The MW3 servers are still up, as are the BBC2 servers.
EDIT: Additional details and remarks.
First, Battlefield 1942 was released in 2002. EA shut down the servers in 2014, primarily because GameSpy - which was running the servers for DICE - went out of business.
Second, ME3 is a cash cow for EA at this stage. When ME:A is released (if ever) they can expect that many people who never played ME1/2/3 will buy the trilogy and play through them. They also like people getting hooked on ME3MP because it makes it more likely that they will be hooked on the series and get ME:A as well.
Finally, since this assertion about the servers being shut down keeps coming up, I would really like to see concrete info from a reliable source that suggests this is being planned, particularly because it does not fit either the business model or the pattern of behavior of EA in this regard.