If the lender (bank) only has to recover 80% of the Purchase price plus selling costs, they shouldn’t be too fussy if the valuation is not quite up to the selling price. If the borrower’s capacity to repay is strong then the risk is low for them. So why wouldn’t they approve a loan even if the property was valued at 90% of the purchase price. So unless you get the lender to confirm the valuation was 100% of purchase price you don’t know what they valued it at. When using a lending broker the broker can sometimes discreetly mention the valuation because they have seen it.

If you had an independent valuation can you expect that the independent valuer will not look at the asking price as,part,of,their,research to establish the value. I think they would look at the asking and purchase price. I would be keen to hear experienced players comment on the differences between lender valuations and independent valuations.

If you look upon the independent valuation as another insurance then it may be worth it especially if it is something you will worry about. Small cost for quality sleep. However for an investor who has to balance risk and costs there is the question of how much confidence do you have in your ability to compare similar properties. And how much insurance do you buy before it becomes uneconomical.
For lower cost housing the reports and valuations can represent a more significant cost than for a median Sydney property. i.e. $400 is a more significant percentage of a $200,000 unit in a regional city in NSW than a $600,000 unit in Sutherland Shire in Southern Sydney.