People love the Super Tiger, but it was a paper plane. The Mirage is superior to the Crusader, the Drakken looks good on paper but it didn't sell well which makes it suspect in my eyes. The Phantom didn't become available for export until 1964 and then to the very specific customer in the RN, the F106 was never exported or even put into service in big numbers (for the USAF) and the Lightning lacked the support of the British Government. In reality the competition was between the F104 and Mirage and Mirage was a better plane, and if well flown (which it would be in RAAF service) could be put up against any of those suggested aircraft with a good chance of success.
The RAN wanted a SAGW ship, in the terminology of the time, and was a traditional buyer of British ships. This is what put the County class on the menu, not that it had command spaces, communications and staff to lead other ships. If the RAN really wanted DLGs then the US Leahey and Belknap classes would be on the menu alongside the Counties. The fact that the RAN looked at the Brooke class and rejected it at least in part because they didn't fit the schedule shows what the RAN was really looking for, regardless of what RAN members who don't have to worry about budgets, manning, building schedules and priorities might want. The Adams class provided a comprehensive SAGW ship within the RAN's budget and manning constraints without the crew and cost overheads of a DLG and the schedule slippage and poor capability of the DE/G.
As for a Tartar conversion of a Battle or Daring, while these may be cheaper than new ships they often don't represent value for money. Such conversions often come with limitations compared to a new build, have a shorter service life and do not represent an expansion of the Navy in a growth period.
To the average person, if a ship is painted grey, it is a battleship. Sadly, this also applies to the average politician.
In my initial postgrad studies, conducted by retired O-5/6s from Army, RAAF and RN (yes RN not RAN he was a Scot), a common narrative was the RAAF and RAF were much better at staff work and selling capability to politicians than the other two services. They were more of the belief that history proved their value to be self-evident.
There is always a temptation to assume the choice made was the best choice and the unsuccessful options weren't really viable.
The RAN needed more ships, they needed area air defence missile systems, and they needed balanced ships with command spaces. They also needed submarines, fighters, ASW aircraft and helicopters, and strike aircraft, but money was limited.
There is a temptation to focus on platforms and specific systems, often with the benefit of hindsight.
The truth is the Mirage was better than the F-104, but it was not as good as it could have been. It is also true there were better aircraft our there. The F-4, wasn't to my knowledge, restricted from export, as I understand it, it was offered to Australia as a Sabre replacement and then again as a Canberra replacement. Nor was the F-106 restricted. The Draken was looked at in the initial assessments but determined that it wouldn't be available in time, for some reason it was not revisited following the delay of the program and the F-104 buy not going ahead.
Many, perfectly good enough, types would have been better than the last batch of Sabres, including significantly evolved Sabres. FJ4 Fury, Super Sabre, Super Mystere? There were options that could have enabled a continuation of a flying reserve, Folland Gnat, Etendard and N156F.
An Alt History I have played with is the RAAF leased two Sqns of early model Lightnings instead of buying Bloodhound. It was never on the cards, never even discussed, but why not?
The RAN did prefer Tartar to Sea Slug, but Tartar, like Terrier and Talos, was not a very capable or effective system at the time, in fact the performance of these systems was so bad the USN was looking to replace them with Typhon. They were eventually made more reliable and capable after a long and expensive "get well" program, then progressively replaced with the much-improved Standard Missile family, which was fortunately compatible with the existing launchers, although much of the rest of the systems needed to be replaced.