Whether or not the servers are on really has nothing to do with buying a new system for 'modern' games- eventually we'll get pushed to buy a new machine just becuase new items will quit getting released for old systems, even if they keep things online for the prior games.
As far as getting a new machine when the older ones quit receiving support- it's gonna depend on what's coming out, how much the systems are, if it's digital or physical, etc. Same as with the last couple generations.
Now, considering the use of these machines after the servers go down... that remains to be seen. We really haven't had a properly online system go down just yet- the Wii was kind of a taste, but it didn't have the same focus on online as the 360 or PS3 did. How many games will remain playable without their day 1 patches? What happens when your system can't check your account to verify you have the license for your downloads? What if your hard drive dies? I feel like, unless Sony/Microsoft patch out some of their protections to give us free use of our data before they take everything down, these systems stand a real chance of becoming paperweights in the future. Well, unless hackers & pirates crack things open for us instead. I can see rom sites evolving into data miners, pulling old update patches off of secondhand hard drives so people can continue to use these old games after the original servers are gone.