Insurers will always opt to replace the instrument, rather than give a cash settlement. Almost always, if cash in lieu of repair/replacement is considered, it will be on a contribution basis only. That's certainly one reason why things need to be insured for what they are worth.
Why should an insurer allow you to under-insure? For example, if you choose to insure a £5000 bass for £100, yes the insurance company will only pay £100 in the event of a claim for theft. But think also of the increase in risk, a bass worth £5000 is a lot more likely to be stolen than a bass worth £100, so the insurer would want a higher premium for that extra risk.