The reason is simple. That peak, Milne believes, could have been a lot higher but for his treatment at the hands of one man – Jim McLean, his manager at Tannadice.
Now 48, Milne has had to fight addictions to alcohol and gambling, and addresses the subject candidly in his newly published autobiography. Those two vices, he admitted yesterday at the launch of the book, are at least part of the reason why he has no money to this day.
But, having confessed to being his own worst enemy on occasion, he is unflinching in his conviction that McLean did him more damage. What is more, he contends that by treating him badly, the manager may also have harmed the club he served from 1971 to 1993.
What's It All About, Ralphie? offers the considered, polite version. "I loved United but the stark reality was that my personality clashed too much with Jim McLean's and in that scenario there was only ever going to be one winner," he writes. "I refused to change the person I was and he knew I wouldn't back down to his tyrannical ways.
"The result was fewer and fewer first-team games and, for my part, a strengthening bitterness towards him. It didn't make for a healthy, professional relationship."
In conversation at Tannadice yesterday, however, Milne gave full vent to that bitterness, and expanded on his assertion that McLean was tyrannical. "There was an old gym here we used to use," he began.
"I once got fined a week's wages for leaving the light on. And I was never in the gym. That's the sort of thing I was trying to deal with, believe you me. It was a waste of time (trying to argue with him]."
United under McLean were known for tying young players to lengthy contracts, and Milne jokingly claimed that he was in fact still on the books at the club he joined on an 'S' form in 1976.
"I've got a copy of my contract. I think it's 25 years with a 25-year option. I think it runs out when I'm 50 – I'm not sure."
More seriously, Milne blames McLean for his failure to win a cap. Regarded by many as one of the most naturally talented players of his generation, he certainly had as much ability as many who played for Scotland – and far more than a few. He is arguably one of the most gifted players not to have been chosen for the national side, and cannot forgive his old boss for what he believes is his role in keeping him out of the squad.
"The World Cup I should have been at was in 1986. I was working in a plastics factory instead to earn some money.
"I'm very bitter. I should have been capped after we beat Standard Liege here. Jock Stein was sitting in one of the boxes and I thought I was a certainty to get into the squad.
"Nuh. Took me as an over-age player in the under-21s.
"I don't like saying anything bad about other players – if they're getting capped for their country, good for them. It's just the case that I should have been there."
McLean went on record in his own autobiography in 1987 about Milne, calling it a tragedy that the player did not become a regular for Scotland. "He had tremendous talent – and I failed with him," he wrote. "He did not have the right attitude to the game and I could not instil that into him."
But if that verdict hints at a certain sympathy towards the player, it is not reciprocated.
Milne may well write of "a strengthening bitterness", but as he remembers it, this was no friendship that slowly soured.
Asked if he had ever got on well with McLean, he responded dismissively. "The only time I got on with the manager was in the summer when I was on my holidays," he said.
Given such rancour between the two men, the wonder is that Milne lasted a whole decade at the club before eventually being sold to Charlton Athletic in 1987. He maintains that if McLean had tolerated him for just a few months more, United – who had been league champions in 1983 and reached the semi-finals of the European Cup the following year – might have won the Uefa Cup in that 1986-87 season instead of being runners-up to Gothenburg.
"I played against Lens and Hajduk Split. The writing was on the wall for me then, so I went to Charlton. I was forced out.
"I went to Charlton and United got Barcelona. I went: 'I can't believe this. I'm playing for Charlton and they're playing Barcelona'. Frightening.
"I scored 15 goals in 42 European games. I'm convinced myself that if I'd stayed here we would have won that."
It was hardly all downhill for Milne after he left Tannadice, for after a year at Charlton and a briefer spell with Bristol City he was signed for Manchester United by Alex Ferguson. And the money was a bit better at Old Trafford than it had been back in Scotland.
But at Dundee United, Milne had been an integral part of a successful team – and also a happy team, for much of the time. In that sense, the end of his stay there brought the curtain down on his meaningful career. He was 26.
What's It All About, Ralphie? by Ralph Milne with Gary Robertson is published by Black & White Publishing, priced 14.99.