What I am assuming is that with a FIS, you know that somebody cares about where you are and what you are doing in case you suddenly go quiet (alerting service). Is there more to it than this?
A FIS implies an alerting service. So if you go quiet for a long time they might start looking for you. If you have a FIS from London Info and are crossing the channel, for instance, they will ask you for your ETAs at various points and if you don't meet those ETAs they will definitely get worried and follow their procedures for that.
So as soon as you've established a Flight Information Service (or any service higher up the chain, like RIS or RAS) it is automatically your responsibility to sign off with that station as well.
Furthermore, once you have established a FIS you will almost always get the relevant QNH without asking. If you have given your route and altitude and the FIS has the capacity for it, the FIS officer will check it and warn you of any infringements you are maybe going to make. If the FIS officer knows your destination and then learns about something happening at your destination (runway closure due to accident perhaps) he will contact you and inform you about it. A while ago I was departing Duxford to cross the channel and the weather looked iffy. So I asked for the very latest METARS from London Info, which were duly presented. But without asking, half an hour later London offered to read me the METARs that were just issued then. And on that same flight London contacted me twice because other ATC units had me on radar and wanted to ask me a question. (And no, I did nothing wrong.) They can also open, close and modify flight plans for you and in some cases London has called airfields on behalf of planes in the air for PPR. Typically in diversion scenarios. They really can be quite useful.
All this doesn't happen if you don't establish a FIS.
But even without establishing a FIS you can ask this sort of information. You are then not establishing an Alerting Service with them so you don't have to sign off when changing frequencies. The station just gives you whatever you require (the local QNH, a QDM, the status of a danger area) and then forgets about you altogether.