True...But the old mechanical gyros based INS absolutely hated that method of start up.
Each INS system, old or modern, prefers to start up where it is allowed to locate its current position
DESPITE memory of its previous location prior to shut down, and every system does have that memory. That does not mean the previous location is not used. It is used to provide a quick reference after the gyro completely spooled up to full rpm. But if the jet is moved, even from the front to most rear row on the flightline, the longer the physical distance, the longer it will take to recalculate or discover the (new) current position. Ring laser gyros do have this issue but the time difference is negligible while the old mechanical gyros may require up to an extra minute to align to the new location.
Here is an example...
Micro-electro-mechanical-sensor inertial navigation system-assisted global navigation satellite system receiver acquisition scheme and performance evaluation - Springer
Note the highlighted.
The article talked about using an external source such as GPS to assist in reducing the alignment time and was between 'cold' and 'warm' start. Back in my F-111 days, we did not have such options. The INS was mechanical gyros based and while an INS cold start take-off was theoretical, the base must have bombs exploding all around in order for any aircrew to fly from an INS cold start.
An INS cold start is essentially you tell the INS to use its previous calculated position then constantly changing aircraft physical location while the INS tries to align itself. The position changes as detected by the gyros must be kept in memory while the INS computer try to compensate for the constant changes based upon that previous location, which may or may not be true. The lower the memory capacity, the greater the degradation of that update capability and most assuredly will not give the aircrew accurate INS data from simple A-to-B navigation to complex bombing runs.
There are plenty of band-aid fixes and patches to allow increased INS cold start accuracy, such as this mathematical mean...
On-the-move alignment for strap-down inertial navigation system - ResearchGate
An INS cold start, meaning on-the-move (OTM) alignment, can actually produce hardware failures, from the gyros themselves such as lockups, or voltage spikes that will cause internal failures of electronic components such as resistors or programmable logic controller modules. Backshops hate INS cold starts and good shops will be able to tell what happened.