I had the issue as well 15 years ago with AF in CDG, they were willing to do it but the system did not allow them. The issue is certainly that HEL cannot issue a luggage tag where HEL is printed.
Then imagine the RIX HEL flight is cancelled or delayed, or you miss the flight, your bag is checked in and they need to retrieve it, so quite a lot of hassle for them. But it could also be that the system does not allow it since it could help you skip the first segment, even if you were not going to do so. However, after you have flown RIX HEL, I am pretty sure you could check in a bag in HEL to SIN and BNE.