When does a 'loan word' cease to be defined as such?

Loanword is defined in the following way in Merriam Webster:-

a word taken from another language and at least partly naturalized

On that definition, there would be no point at which, say, the word naïve (the feminine form of the French word naïf) can cease to be a loan word. Even when it is fully naturalised, it remains at least partly naturalised.

Cambridge English defines it thus:

a word taken from one language and used in another

This definition is even more permissive than the American one.

It leaves some uncomfortable implications to this definitions, which, I think, have some force.

Many are surprised to learn that the humble bungalow is a loanword from India, as are our pyjamas. On the above definitions, they must be regarded as loanwords, like the good old double decker bus (the vehicle for everybody, for which the Latin is *omni***bus**.

And what about the language of science, brought in without charge from ancient Greek (philosophy, rhetoric, oligarchy...)? Are these not loanwords, even though they come from a different language? Or do we give Greek and Latin vocabulary special immigration status as part of the Anglo-European linguistic empire?

So I am inclined to agree with those who have suggested that at some point we cease to think of words like café a foreign and drop the acute accent. So tea, chess and etcetera will be fully native English (of whichever national variety), with a nonetheless rich and fascinating ancestry.

Meanwhile, from the other side of the loan, other languages look (at least to us) a bit less well integrated. So in modern Greek you watch television relaxing in to livingkrum. You might have a sail in to giot (unless you are willing to use the more windy skaphos anapsychis - literally vessel of wind). Your trousers are Italian pantalonia, and your suit is a French kostoumi. If you want a cup for your tea, you ask for a Turkish flintzani.

We should probably exclude from the family of loanwords new the Greco-Roman language of science and law, as well as key technological inventions like the internet, computer etc. Languages handle these with varying preference given to convenience, inventiveness and national or ethnic pride.

A tighter definition of loanword might be helpful. Or it might take us round in circles.