I really wish it had been Ackbar. He deserved better than a death where you don't even realize it happened until minutes later.
As far as the droid (or autopilot thing) goes, I agree from a logical point of view, but not a dramatic one. If I had to change the scene but keep it as much alike the finished film as possible, it would go like this...
They are all piling onto the escape pods, the plan is to fly off in the shadow of the main ship so as to avoid detection. They mean to leave the ship just running straight ahead and for everyone to leave.
The ship is massively rocked by the barrage of blaster fire they've been raining down on the for (days?) ages. The bay is compromised and the last pod has to leave immediately. Ackbar or Holdo are too far from the pod to make it before it is lost so they activate the launch and stay behind. They duck out of the bay just as it loses integrity, the pod also just making it.
Some of the blaster shots start peppering the pods, so Ackbar-Holdo double-times it to the bridge, laying the ship into a curving turn to better protect them. Only as it comes about do they (we read it on their face) decide to take 'er in. The tragic hero music plays as they sadly initiate the jump. The ship is breaking up around them, the bow on fire and the First Order cease fire when it's clear that the fight is done. The jump is a million to one shot and the ship breaks up even as it jumps, spraying lightspeed debris over the entire fleet.
It's far from original, but I can imagine it being quite a thrilling moment as opposed to Holdo saying she had to stay behind to pilot the cruiser and then showing her mostly just standing in the middle of the room doing nothing. And yeah yeah...I'm not much of a writer, I know that.