The Australian-English phrase silly as a wheel means extremely silly.

For example, Patrick Smith used this phrase punningly in Rocky road as Tyler-Sharman ordered out, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Saturday 19^th September 1998:

On your bike Lucy Tyler-Sharman. That was the order by Australian Commonwealth Games chef-de-mission Don Stockins at an extraordinary media conference yesterday afternoon. Now she’s on a plane back to Perth, incensed and in disgrace.
Australian cycling, you see, is silly as a wheel. At these Games some of our competitors can’t keep their feet on the pedals, ignore team plans, miss their start times, crash, and allude to sabotage by team administrations. Just as well they bus them to the velodrome and track. They would be no certainty to get there if they had to ride. It is unclear why we call them a team at all.

It seems to me that the Australian-English phrase silly as a wheel can be compared to British-English phrases such as daft as a brush, daft as a swill [i.e., a big basket], daft as a gate, daft as a wagon-horse and mazed as a broomstick: I think that, in those phrases, the underlying notion is that anything is silly that does all the hard work.

The earliest occurrences of the phrase silly as a wheel that I have found are as follows, in chronological order:

1-: From Smoke Signals from the Never-Never. Cattle Thieving Up-To-Date, by the British-born Australian author William Hatfield (1892-1969), published in the Sunraysia Daily (Mildura, Victoria, Australia) of Monday 21^st December 1931:

I asked who was the joker with two horses camped almost in sight on the edge of some thicker scrub not a quarter of a mile away.
“Oh him?—Old fossiker, a Hatter, silly as a wheel, carries a gun, liable to shoot anybody goin’ over for a yarn—might wing yer Chevrolet too!” Well I don’t know pust [sic] how silly a wheel may be, but I had seen cranks who were obsessed by the idea that any stranger might do them harm, so I accepted the explanation.

2-: From Cheering up the World, by ‘Madam Wu’, published in The Chronicle (Adelaide, South Australia, Australia) of Thursday 2^nd September 1937:

I am a pretty happy sort of being—in fact, in the district, I am regarded as being as silly as a wheel and as carefree as a pound of cheese, but some people get on my nerves with their grumbling.

3-: From Night Flight, a short story by Alan Mitchell Stephens, published in The Western Mail (Perth, Western Australia, Australia) of Thursday 8^th November 1951:

The Captain stopped in his pre-take-off inspection of the interior of the Pegala, en route to the Eastern States. He and the second pilot were in the Air Hostess’s cubby-hole. He picked up the red-covered book, and read the title, which caused a low whistle of surprise. He turned to his offsider.
“Clare’s really excelled herself this trip—‘The Case of the Giggling Ghoul.’”
The second dickey snorted his disgust. “Can’t see what she sees in them, must be as silly as a wheel.”

4-: From The Ridge and the River (1952), a World-War-II novel by the Australian author Tom Hungerford (1915-2011)—as published in The Sunday Herald (Sydney, New South Wales, Australia) of Sunday 6^th July 1952:

“What do you think of your mate now, Alec? What a God awful show—remember what I told you in the hole last night?”
“He’ll be all right,” Shearwood said with affability he was far from feeling. Oscar was sound, but silly as a wheel. “He’ll settle in O.K. once he gets his bearings.”

5-: From Riverslake (1953), by the Australian author Tom Hungerford (1915-2011)—as published in The Mail (Adelaide, South Australia, Australia) of Saturday 29^th August 1953:

“Slim’s the best bet in the kitchen—he’s only a boy, and he’s silly as a wheel, but he’s got it here.”

6-: From a correspondence by Red Smith, from Melbourne, Victoria, Australia, where the Olympic Games were taking place, published in The Boston Daily Globe (Boston, Massachusetts, USA) of Tuesday 4^th December 1956:

Ah, it was bonzer, as most other aspects of this visit have been. To be sure, the tourist can complain with justice about the Waldorf prices which some of the sleazier scratch houses have put on for the duration, and if he came down with only tropical weight clothes expecting Summer temperatures, then he was silly as a wheel.
Sometimes the sun shines, but by and large when you speak of the weather you have to say the game is crook at Tallarook and there ain’t no work at Bourke.

7-: From Aussie English: an explanation of the Australian idiom (Sydney: Ure Smith Pty Ltd, 1965), by the Australian author John O’Grady (1907-1981):

GALAH
A grey-backed, pink-breasted inland parrot, gregarious and noisy, destructive and useless, and considered to be ‘as silly as a square wheel’.
Any human beings who possess these characteristics—particularly drivers of vehicles other than your own—are ‘galahs’.
Most human galahs are young. If their galah habits persist, they may graduate, and become dills, or nongs.