I did some more checking and discovering this week and got some valuable feedback from my webmaster customer/contact. It's straight forward to change the definitions for alignment in TinyMCE.
Tiny even does this in the example they have online in the documentation for custom formats at https://www.tiny.cloud/docs/demo/format-custom/
"classes": "text-left", "block": "p"},
"classes": "text-center", "block": "p"},
"classes": "text-right", "block": "p"}
alignleft is a built-in definition to which the TinyMCE formatting menu, buttons etc. refer by name. If you override it like above, Tiny will use the class and not fill the style attribute.
The css-classes used are 1:1 matching bootstrap 3-4 classes for alignment. With the current efforts for Plone 6 to modernize Barceloneta to a new 'bootstrap 4 classes only' theme , this is isomething that can also be taken into account.
I also checked more on use of the 'style' attribuut in general. Apparently before IE 11 the style tag was not only a layout/visual but also security concern in some browsers for extranet/public sites. You could import css and do other nasty stuff. This was before CSP (content security policy) was introduced.
The Cleaner class in lxml still removes these kind of security related css content in the style attribute, also in current Plone 5.2 if I undestand correcty from Maurits' checks and previous post.