There is a third reason: Stove installers these days insist on lining chimneys because it then means they don't have to take responsibility for the condition of the existing stonework. Also, as you've noticed, they can charge an arm and a leg for installing the liner!
As Creagan says, the reason for insulating the lining is to reduce heat loss, thus keeping the flue gas temperature high. This basically makes the flue gases more buoyant, and increases the draw. Insulation can be either loose fill (vermiculite flakes or ceramic malteesers) or wrapped insulation jackets. The advantage of loose fill is that it's easy to do, and because you put it in after the liner, it doesn't make it any harder to fit the liner itself. The disadvantage of vermiculite is that it holds water (that's why it's also used as a soil improver), which can cause problems with stonework if you have any water penetration. The advantage of the insulation jackets is that they are mess free, and also protect the liner from puncture or denting during fitting. They are expensive though.
When we fitted a stove in our house, we found fitting the liner very easy indeed. The only problem was that when we poured in the vermiculite, it started coming down the adjacent fireplace too (oops! obviously a breach between the two chimneys somewhere). That meant that we then had to line the second chimney as well, and fill both with vermiculite

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The stove installer had quoted us £1175 to supply and install the liner, plus £545 for chimwrap insulation, so that would have come to a shade over three grand to do both chimneys

. Since even doing one of them was way over our budget, we bought the bits from hotline chimneys and installed them ourselves. That saved us about 2 grand all in all, so it's pretty significant. Note, I'm not saying everybody should DIY - just thought I'd explain what we did, in case it is of help to others.
And the result? Just the act of lining the chimney turned the existing stove in the second fireplace into an absolute rocket, so much so that we melted holes in the ashpan the first time we re-lit it with the liner in place! Definitely worth doing IMHO!
Hope that helps!