If you take away insurance, the basic legal rule is that if one person wrongfully causes damage to another, the wrong-doer can be compelled to make the other part "whole", that is, undo the damage that they caused. If you have an item of property that would cost $3,000 to fix or repair, then you could be compelled to pay for that repair or replacement. Even if it is decided that the wrong-doing party is entirely liable for the damage, there can be disputes over what that amount of damage actually is. "Bluebook" is one means of standardizing value, but it is not an actual legal definition of what a given car is worth. Really, it just depends on whose evidence about value is most persuasive. An insurance company is motivated to pay the least, and the aggrieved party is motivated to receive the maximum. A jury can weigh the arguments and decide on a figure.
If indeed the cost of repair is objectively around $5,000 and the cost of replacement is similar, then a jury would most likely find that that is what the at-fault party is liable for. So the way to "force" an insurance company to increase their offer is to persuade them of two facts: that the costs really is about $5,000, and that you are willing to sue their client to recover that $5,000. An insurance company simply covers their client's liability, so if the damage is $5,000, you don't sue the insurance company to get more, you sue their client. You have no obligation to accept an offer from either the insurance company or from their client: but if you don't accept some offer, you will have to sue the client to get anything.
Bear in mind that in Missouri, they follow the theory of "comparative negligence" which means that if A is found to be 75% at fault and B is 25% at fault, A is liable for 75% of B's losses. The police report does not decide that, rather that is determined by the trial. The police report is relevant to determining who gets a ticket, if anyone: civil liability is determined via a lawsuit.
Putting this all together, offering $1,400 may be a strategy – a simple solution where you just accept that sum and move on. A more complicated solution is to not accept that offer, making it clear that you intend to pursue the compensation that a court would award you. If you hire an attorney, they can give you practical advice on what a court is likely to award you, how much it would cost to take it to court, and of course they can write an effective letter to the insurance company making an appropriate counter-offer.
