Easier said than done!
Even a short range missile like Tayfun needs 456 seconds to travel 561 km. That time also includes the suppressed trajectory altitude it needs to get up to and down again to cover a straight line distance of 561km. The actual burn time of the fuel is very short. Not in minutes but in seconds.
According to observers, Bora missile’s initial launch time was shorter which indicates that although Bora and Tayfun share the same canister and are similar in appearance, Tayfun’s slower burn in launch helps it to retain more fuel and more energy to be used in thrust for extended burn times, increasing range and speed in upper atmosphere.
Also, a ballistic missiles’ embedded gyroscopic guidance system would experience trouble in calculating the flight envelope, if the range is increased. It gets more challenging to make fine gyroscopic calculations at higher velocities too. Hence, improvements in the missile’s inertial guidance and software infrastructure will also improve combustion efficiency. This returns as better energy potential and range. So software improvements help with range and midcourse speed.
As ballistic missiles are most vulnerable in boost phase, it is better to keep this phase away from prying eyes and AD systems. It is most difficult to intercept a ballistic missile travelling at hypersonic speeds during its midcourse. So rather than firing a missile close to our borders, it is better to fire it from inland to allow it to attain untouchable speeds when over enemy airspace.
To keep some of the fuel for terminal phase means, you need to expend more fuel to launch a heavier load. Hence bigger and more expensive missile. If we are talking about a two stage missile, it will definitely be an expensive exercise.
The whole idea behind ballistic missiles is the fact that it utilises the rare, almost drag free upper atmospheric conditions to gain speed and with the altitude it is at, it can dive and increase speed further. The trick is to make the dive as perpendicular as possible to decrease air drag at lower layers of atmosphere and conserve energy.
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What you are suggesting is like a dual pulse engined rocket which waits for the second and comparatively smaller pulse to be engaged at the threshold of dense atmospheric layers ; May be at ~15km altitude? If the missile reaches this altitude with a speed of 1500m/sec, to sustain this speed till it hit the ground, second pulse will have to be active for 10 seconds. That is still a lot of fuel.