Leave all the architectural charm you can. Don’t remove it unless you have a specific, spectacular idea to replace it.

Would need to know, replace with what, but as a rule keeping the historical or removing it and leaving it empty makes more sense than a replacement. I do see a disconnect in the scallops/corner caps/scrolly work so understand your motivation. Seems like the dental work on the chimney if painted out would coordinate with the corner caps. I wonder if I would prefer dental trim to the scallops but in the end I think its just too much. Keep looking on your paint choice.

No, keep all that architecture. Let the house look like what it was intended to look like. Also, no blue on it, a nice cream color stucco fits your house far better than the blue. Dont take away all its character.

@chispa, the house was built in 1937. BTW, we added that Decorative plasterwork/ornament ourselves (about 10 years ago). The original house didn't have anything there which looks quite odd when comparing with the neighboring houses. Here are some photos of our neighboring house:

All the faux Mediterranean houses in my area have those fake quoins and people are now removing all that added on fake stuff when they remodel.

I would return it to what is was meant to be, without all that overdone wedding cake icing! Improve you curb appeal with hardscape and landscape.