That's quite interesting!
I have similar observations with sqlite in Conquest as well. No joint indices but its speed didn't really degrade at all as database grows bigger.
However I have seen sqlite's performance degrading in other software applications which can be recovered by the creation of joint indices - I guess it depends on each individual use case.
In case of help, the statements I used were:
CREATE INDEX idx_patientid ON dicomstudies(patientid);
CREATE INDEX idx_patientid_studyinsta ON dicomstudies(patientid, studyinsta);
CREATE INDEX idx_studyinsta_seriesinst ON dicomseries(studyinsta,seriesinst);
CREATE INDEX idx_seriesinst_sopinstanc ON dicomimages(seriesinst, sopinstanc);