You should note that electors are generally party loyalists who will not vote faithlessly. Very rarely, there are some who vote faithlessly and they will be either punished by a state or by their political parties. In other words,
a faithless elector runs the risk of party censure and political retaliation from their party, as well as potential legal penalties in some states. Candidates for elector are nominated by state political parties in the months prior to Election Day.
[Wikipedia: Faithless elector]
There is no Constitutional provision or Federal law that requires Electors to vote according to the results of the popular vote in their states. Some states, however, require Electors to cast their votes according to the popular vote. These pledges fall into two categories—Electors bound by state law and those bound by pledges to political parties.
[Source: About the Electors in www.archives.gov]
Why is it that these electoral college votes are not secret?
As explained in the link and quote, they are bound by state law or have already pledged to political parties. They are party loyalists and they don't mind their votes being not secret. To their view, they are not voting their conscience, they are voting as pledged or bound.
Could a state decide to make it secret by allowing electors to, for instance, stick their ballots into a box and shuffle them before being counted?
Again, there is no reason to make their votes anonymous as the election result is de facto decided by the popular vote and electors vote just to confirm the result.