From the Reason.com article: "On January 4, 1961, a state judge, Ronald Jamieson, retroactively validated the Democrats' seemingly premature certificates. According to Jamieson's ruling, it was crucial that the electors had convened on December 19, even though their certificates contradicted the official results at the time. Two days later, while overseeing the congressional tally of electoral votes as vice president, Nixon acknowledged that he had received three sets of certificates from Hawaii: the dueling December 19 slates, plus a subsequent Democratic slate that Hawaii's governor certified after the recount. Nixon concluded that the third slate, comprised of the same Democrats who had signed the December 19 certificates, "properly and legally portrays the facts with respect to the electors chosen by the people of Hawaii.""
There is not an indefinite amount of time - or even a very long time - to challenge presidential election results. Obviously it wasn't silly in 1960 - the contingent slate was crucial to a proper accounting of Hawaii's result. The electors have a specific date on which they have to meet, vote, and certify. There's also a fixed date by which the certified votes have to be received by the people who receive them. Obviously a challenge can continue past the first date (I don't know about the second), but without the electors' certified voting results being received on time, there's no point. As long as the formality of having actual electors persists, the value of allowing a contingent slate to properly prepare its vote persists, as does the value of allowing the result to be "transmitted to Washington".
The public outcry over losing electors occasionally certifying a result and sending it to Washington is probably nothing compared to the public outcry if an overturned state result capable of flipping an election eventuated and the (completely correct and legal) response was "Sorry, the electors didn't vote on time/didn't get their vote to Washington on time". Allowing the certification and transmission is a safety valve.