Why were bowsprits fastened with loops of rope?

[UVSaturated]

Did this serve some other function?

 

[Uwek]

The function of these loops were to hold the bowsprit down against uplift forces.
Take a look at your first photo:
Imagine wind forces in the jibsail - the sail is pulling the bowsprit - and to keep the bowsprit in place it has to be fixed - the correct term is gammoning



Taken from

http://www.woodenboats.lt/Knygos%20public/Modeliavimas/Ship%20Modeling%20Simplified%20Part%203.pdf

 

[albertmary]

They allowed the stays to be made tout as much is required to prevent the raked foremast to fall while carryng its square canvas and the staysails to get their proper wing-shape via reducing the sag. Martingales got the same effect on jibstay and its sail