The first published (!) BASIC dialect that came without line numbers was the Amiga BASIC in 1985, as far as I know - and this is a Microsoft-BASIC. One year earlier some Apple engineers worked on an "Mac BASIC" which did not use line numbers either - but was never published since the Apple company had a contract with Microsoft to produce their sole BASIC for Macs.
Many professions, especially any that deal with ancient texts use line numbers, or paragraph numbers. The Bible uses verse numbers, the Lutheran Confessions of the 16th century, uses paragraph numbers, and many official referendums and memorials proposed using Roberts Rules of Order, will use line numbers for ease of floor amendments during a meeting, convention, or convocation.
Like your text file example, the Burroughs time-sharing system used line numbers on Algol programs too, even though they weren't part of the language and were only there to help edit the file.
The use of line numbers was not invented by the BASIC developers (Tom Kurtz and John Kemeny). In the 1978 article written by Tom Kurtz for the History of Programming Languages conference, he mentioned they looked at JOSS and their use of line numbers which also had decimals (ie a line could have the form NNN.NNNN) but reject the form so only allowed integers. I guess it made it easier to teach and implement, but did force more of a requirement for a program to RENUMBER the source code (and change all the language references to be correct -- hence the editor needs to keep up with an language changes) (Confession: I maintained the editor that did this for years, most of them on a volunteer basis)
I believe that Digital Equipment Corporation's BASIC-PLUS language also permitted omitting line numbers in most cases. Or perhaps that was only a feature of DEC's BASIC-PLUS2. Either way, those languages appeared during the '70s and '80s.
I got my start with BASIC-PLUS, and I love that language. I often refer to it as my beloved BASIC-PLUS 😉. I never had the opportunity to use BASIC-PLUS after 1979, and I never used a VAX. I went to the dark side working for IBM on Unix systems.
Microware (not Microsoft) created a multitasking operating system called OS-9 for the Motorola 6809 (8/16-bit microprocessor). Microware also created a programming language called BASIC09. BASIC09 included structured programming features and generally did not require line numbers. This was during the 1980s.
I got an 8-bit home computer and learned to program in 1983. My BASIC was a run-of-the-mill line number-based one comparable to what you'd find on most '80s home computers. The first time I used a BASIC without line numbers must have been in the latter half of the 80s. My father had a PC and got his hands on a copy of Borland's Turbo Basic. Although the concept of a BASIC without line numbers felt alien, I slowly got used to it. Later I used QBasic and Visual Basic, too, but honestly, I never loved structured BASIC the same way I had the old line number BASIC I first encountered. I think Turbo Basics' biggest selling point was, for me, its ability to compile my program to EXEs.
The first published (!) BASIC dialect that came without line numbers was the Amiga BASIC in 1985, as far as I know - and this is a Microsoft-BASIC. One year earlier some Apple engineers worked on an "Mac BASIC" which did not use line numbers either - but was never published since the Apple company had a contract with Microsoft to produce their sole BASIC for Macs.
Many professions, especially any that deal with ancient texts use line numbers, or paragraph numbers. The Bible uses verse numbers, the Lutheran Confessions of the 16th century, uses paragraph numbers, and many official referendums and memorials proposed using Roberts Rules of Order, will use line numbers for ease of floor amendments during a meeting, convention, or convocation.
Like your text file example, the Burroughs time-sharing system used line numbers on Algol programs too, even though they weren't part of the language and were only there to help edit the file.
The use of line numbers was not invented by the BASIC developers (Tom Kurtz and John Kemeny). In the 1978 article written by Tom Kurtz for the History of Programming Languages conference, he mentioned they looked at JOSS and their use of line numbers which also had decimals (ie a line could have the form NNN.NNNN) but reject the form so only allowed integers. I guess it made it easier to teach and implement, but did force more of a requirement for a program to RENUMBER the source code (and change all the language references to be correct -- hence the editor needs to keep up with an language changes) (Confession: I maintained the editor that did this for years, most of them on a volunteer basis)
I believe that Digital Equipment Corporation's BASIC-PLUS language also permitted omitting line numbers in most cases. Or perhaps that was only a feature of DEC's BASIC-PLUS2. Either way, those languages appeared during the '70s and '80s.
https://en.wikipedia.org/wiki/BASIC-PLUS
I got my start with BASIC-PLUS, and I love that language. I often refer to it as my beloved BASIC-PLUS 😉. I never had the opportunity to use BASIC-PLUS after 1979, and I never used a VAX. I went to the dark side working for IBM on Unix systems.
Microware (not Microsoft) created a multitasking operating system called OS-9 for the Motorola 6809 (8/16-bit microprocessor). Microware also created a programming language called BASIC09. BASIC09 included structured programming features and generally did not require line numbers. This was during the 1980s.
https://en.wikipedia.org/wiki/BASIC09
I got an 8-bit home computer and learned to program in 1983. My BASIC was a run-of-the-mill line number-based one comparable to what you'd find on most '80s home computers. The first time I used a BASIC without line numbers must have been in the latter half of the 80s. My father had a PC and got his hands on a copy of Borland's Turbo Basic. Although the concept of a BASIC without line numbers felt alien, I slowly got used to it. Later I used QBasic and Visual Basic, too, but honestly, I never loved structured BASIC the same way I had the old line number BASIC I first encountered. I think Turbo Basics' biggest selling point was, for me, its ability to compile my program to EXEs.