Latest polls predict a hung parliament. This result could also come about with the Tories getting more votes than Labour. Either way, in this situation we could face a constitutional crisis without an effective, independent head of state.
Britain Elects
Apr 11
Britain Predicts — model update
If an election was held today...
LAB: 293 MPs (+91)
CON: 264 (-101)
LDEM: 13 (+2)
An elected head of state with a limited constitutional role can sack a PM (in very limited circumstances), or decline the prorogation of parliament and force the PM to face a no confidence vote. They can also facilitate negotiations between parties, to form a new government. That's how parliamentary republics work and why there's a use in having a separate, independent and accountable head of state. They can guard against crisis and help manage those crises when they happen.
The scenario is
unlikely, but not impossible. Imagine if the result was different, where Labour had 300 seats and the Tories (in power) ended up with 285 seats and no other party had enough seats to give either side a majority. And imagine if the popular vote was marginally higher for the Tories than Labour. This could very quickly lead to the kind of situation that descends into constitutional crisis, where two parties can claim the legitimate right to govern.
Our constitution needs fixing, and we need an elected head of state.