Not in the least bit severe, restrictive or unreasonable. I have no sympathy for anyone who doesn't know and obey the Rules of the Road, knowledge and observance of which is a requirement for driving on Irish roads out of respect for the safety of other road users.There are certainly no severe limitations coming down to the level of detail quoted for that Aviva policy.
IMHO the Aviva contract wording seems very restrictive and unreasonable from the perspective of the reasonable customer.
I still hold a lot of sympathy for OP on the merits.
An appeal to the Ombudsman perhaps ?
Section 4, Page 40 deals with vehicle safety and the driver's responsibilities. In general terms in states:
"There are minimum standards set by law for the condition of your vehicle.
You must know these standards and make sure your vehicle complies with the law. This section sets out the basic information you need to know. For further information on the testing of your vehicle please see www.rsa.ie
As a driver, you must make sure that your vehicle is in good working order. You must ensure that the steering, brakes, front and rear lamps, indicators, reflectors, rear view mirrors, safety belts, speedometer, tyres, windscreen wipers, horn and silencer are checked regularly."
Specifically, in relation to tyres, it states
Tread depth: Do not allow your tyres to wear down too much. Most vehicles on the road must have a minimum tread depth of 1.6mm over the main treads. For motorcycles and vintage vehicles the minimum tread depth is 1mm. However, make sure you replace your tyres before they become this worn.
Pressure: Regularly check the pressure of every tyre, including the spare tyre, and pay attention to the recommended pressure levels. See the manufacturer’s specifications for correct inflation pressure.
Checking for damage: Regularly examine your tyres for cuts, cracks and bulges, which could cause unexpected ‘blow-outs.’
Before you get a flat tyre: Check your vehicle and make sure you know how to change a wheel, that you have a spare wheel and repair kit to hand.
Replacing tyres: For your safety, only fit new and e-marked tyres bought from a reputable dealer. Do not mix radial and cross ply tyres on any one axle. Tyres must be the same on any axle.
Temporary use (space saver) spare tyre or repair kit: Only use these tyres to complete a journey or make a journey to a tyre dealer. Do not travel at a speed in excess of the recommended speed stamped on the tyre."
Appealing on the grounds you specify would make any driver who has had a claim rejected on the grounds of ignoring basic, well-documented safety measures look even less worthy of holding a licence or insurance certificate than they already do in my eyes.
I take it the objectors to the insurance comapny's understandable stance haven't read the Rules of the Road either.