Not true. The warranty is in addition to your legal rights which are covered by the Consumer Rights Act. That says goods must be of merchantable quality, fit for purpose and last a reasonable time. In England that is six years, five in Scotland.
Err, yes and no.
Yes, you have legal rights which are over and above what any guarantee might offer - but these have no fixed length other than "reasonable time". What is reasonable will vary - e.g. you can't expect the same durability from a really cheap TV set as you might expect from a high end (and high price) set. There is however a general presumption that if something fails within the first 6 months then it was likely to be defective at point of sale and it's really for the retailer to show otherwise. After a couple of years (give or take, depending on the circumstances) there would be an assumption that it wasn't a latent fault and it would be for the consumer to show lack of durability. In between it's a grey area.
But, the key point is that consumer rights legislation does not mean that "something breaks down, seller has to fix/replace/refund it".
In fact there are a number of different aspects to consumer rights legislation :
The first is that the item must be as described and fit for the purpose for which it is sold. Mention above of "you shouldn't put wet towels on a towel radiator" would be a complete admission that the towel radiator was not fit for the purpose for which it was sold given that the primary function of a towel rad is to dry wet towels
The second is that at the point of sale the item should be free of faults unless they are pointed out (e.g. marks on an ex-display unit). As mentioned above, there's a general presumption that if something fails within 6 months then it was likely to be a latent defect.
The third is that it should be reasonably durable. And that's where the arguments will happen over what is "reasonable". If the hob was the cheapest pile of tat on the market then after 3 years it could be a tricky one to argue, but personally I would expect any hob to last more than 3 years - assuming the excessive leakage is a fault rather than a "design feature").
What is fixed is that we have a statute of limitations which means that for a civil action you are time barred after 6 years in England and 5 years in Scotland. But this is completely separate to consumer rights legislation. So while you could argue that a high end hob should last (say) 10 years in light domestic use, after 6 years there'd be nothing you could do about a failure as the statute of limitations would kick in to protect the seller from a claim.