Why Nuclear Power At All?

When it comes to Nuclear Power, i am very much undecided as on the one hand it is clean energy compared to fossil fuels but then it does create waste which remains dangerous for tens of thousands of years and if their is an accident at the plants...all out disaster, the Chernobyl nuclear disaster in 1986 spread radiation across Europe and substantial parts of Belarus and Ukraine are still cordoned off today.
A poll by YouGov 40 years on from the Chernobyl nuclear disaster, shows that i am not the only one with Britons divided on whether nuclear energy is safe.
The Government have recently given the green light to a new power station in Anglesey but around half of Brits (51%) generally support the use of nuclear power with 37% saying we should actively be getting more of its energy from nuclear with 23% believing the UK should reduce the amount of electricity it gets from nuclear energy.
The big take away is that nuclear has fewer enthusiasts than renewable energy sources with 55% wanting the UK to get more of its energy from onshore wind, 63% favouring more energy from bio-fuel and geothermal sources, 67% wanting more offshore wind or hydro-electric power, and 73% backing more electricity being generated through tidal and solar power.
As the Chernobyl disaster demonstrated, nuclear power stations do have the potential to go very badly wrong and 45% believe that today's nuclear energy is typically safe and it may well be but the highly toxic waste, currently we have 4.58 million cubic meters, enough to fill Wembley, which we are struggling to deal with (currently it is in storage while trying to develop a long-term solution to bury it) which has a half life ranging between decades and 100,000 years so until that problem is sorted, generating even more seems we are merely switching a problem of polluting the air to polluting the ground.
Why we are not putting as much money and resources into renewable sources as we do nuclear is a question for the politicians but it does seem madness to be looking at a nuclear answer when ramping up the much cleaner and safer wind, solar and tidal power is the obvious solution.