It all depends on the nature of the policy -- with different procedures often applying depending on whether it is an individually purchased policy or a group, such as employer provided policy, and the particular insurance company.
Among the reasons some insurance companies prefer to wait until all the forms are in is that it makes paperwork easier and it reduces the possibility that one of the beneficiaries might have a claim to more than what the insurance company regards as his or her share of proceeds.
Many companies, as a matter of practice, simply pay as the claims arrive, assuming there are no questions open. The vast majority of death claims arise on policies that were in force for over 2 years (so the policy is incontestable in 99% of all cases, even if the applicant had lied about his or her health), there is no issue about the insured being older than he or she said on the application, or being of the opposite sex, and there is no suggestion that a beneficiary may have killed the deceased, there is no need to delay the basic benefit. Assuming that the policy did not contain an accidental death benefit -- the old double indemnity -- and thus further investigation is not need, companies are quick in making payment.
If the insurance company knows there is likely going to be delay -- such as if one beneficiary is treking through Tibet for a year and this is unavailable -- it surely would not delay at all in paying out the other beneficiaries' share earlier.
Many insurance companies vonultarily pay "delayed settlement interest" from date of death and many sate laws require interest interest if more than a certain period has passed between filing and payment. Also, note that the interest rates involved may be well above market (in January 2004 the average bank was paying in the range of only 1% interest on money market and similar demand type deposits.
If one of the beneficiaries really needs the money, just tell the insurance company. The fact is most will be very obliging.