Changing an oven element is a straight-forward 'fitting' job - it does not need electrical knowledge in the sense that one is not creating new circuits in the way that an electrician is trained and qualified to do.
With a fitting job, one disassemblies the unit, then re-assembles it in reverse.
A handyman is more than competent to do this type of work.
If you look at the small print of the warranty you will almost certainly find that 5 yrs applies to parts only, parts and labour is a lesser length - often 1yr. Hotpoint are thus not reneging on anything.
However you would be correct is assuming that the cost of the part is probably �20 (a guess) so the cost of labour at one hour is thus �99 (another guess) so often far outstrips the cost of the warranty part. If you decline to use their labour service, they probably won't supply you the part - but try it. You can find out the cost of part from a high street repair company and decide for yourself whether you can find another route more cheaply.