I have a view that I should aim to use language in the way that other people use language. Hence I use the definition identified in Wikipedia (and elsewhere)
I accept the point that overstayers did not migrate illegally, but they are known as illegal immigrants in that they are immigrants who do not have a lawful right to be in the country. (ie their situation is illegal). That is the normal usage of the description.
A very very dangerous generalisation - under it all the Windrush victims would have been classed as illegal immigrants in your book - until they proved the law had been applied wrongly
Equally I have a friend here is his background - at the end you can tell me your thoughts
Born Northern Rhodesia to British parents (no birth certificate as none issued there at the time)
Moved to NZ when v.v. young as independence happened
Lived in NZ until early 20's when joined British Army (REME)
Served in Gulf war 1 & 2 mainly based Berkshire & Paderborn where he met his German wife and had child 2002
Moved to UK about 2006
Left army on medical discharge due to knee issues caused by gulf war inoculations straight before a route march (luckily German civilian hospital had kept notes as UK Army medical corps had conveniently lost them all), wife started work to support them
Went to get a passport (didnt need one before) - as no way to prove when he was born and to whom he was offered Zambian nationality, being in the army he had been out of the uk for >6mths too often to have in the eyes of the home office accumulated enough years here. He was able to stay as married to an EU national and his son has German citizenship
Along came Brexit - they have only been offered pre settled status which led to his son not applying to uni last year (no automatic right to lower tuition fees)
So was he an illegal immigrant from when he joined the British Army until he married his German wife ? (because he did not according to the Home Office have any lawful right to abide here)
How about if I said "A Zambian who arrived in the UK via a roundabout route and lived here for well over a decade before he found a way to make himself legal through marrying an EU national - should his child get a UK tuition fee loan ?"