Eagle Speedster, One Flaw?
Would it have been that difficult?
Yes. Look at the very short cowl and distance between the end of the hood and the front of the windshield. If you continue the bulge, you have to get an irregular windshield and do some clever engineering of wiper linkages and such. The triple wiper system would have had to be completely re-engineered, probably for the worse as a double wiper system could not properly wipe the compound-curve windscreen. Your windshield seal would have been more complex and therefore more expensive (urethane window sealing had not reached Europe yet) and of course far more prone to leak. The hood seal would have had to have been molded especially to fit the bulge instead of just a flat strip off the shelf which back then would have been quite a lot more expensive. Then you'd have to make sure the welding around the curve was done right, to say nothing of the increased cost of making the stamps to crank it out. And so on and so on.
This would have driven the cost of the car up considerably.
This was a car that for the era went and looked like a Ferrari 612 but was priced like a Subaru Impreza. They did nothing that was not strictly necessary. Early E-Types don't even have internal hood latching systems; they had external latches bolted to the outsides of the hood and you buckled the hood down with them. Only later when the E-Type was a smash success did they go back and design internal latches for them. Some of the very earliest preproduction cars didn't even have that, they had leather belts instead of latches.
So, yes, it would have been difficult, expensive, and as the sales numbers showed, completely unnecessary. Pretty much nobody notices the cutoff as the windshield visually blends it in from most angles.
Finally, Jaguar (as they did with so many things pre-Callum) turned a necessity into an advantage. Entirely aside from the cost needed to continue the bulge, the bulge serves one more purpose. It's open at the back and along with the two sets of hood louvers, it serves as a heat extraction point for the engine bay.
On top of that, on cold days the stream of hot air out of the bulge helps keep the windscreen clear - something pretty much every other classic British sports car marque failed at due to their anemic heaters. Morgan, for example, *still* doesn't have good windscreen defrost in their Plus Four.
So, extending the bulge would have been difficult, cost them a metric butt tonne of money overall, would have made the car run hotter and worse to operate in winter. Why would this make any sense for them to do?