Yes, it's true that two reasons for double entry book keeping are to avoid negative numbers and to provide a means to double-check any entry.
The prejudice against negative numbers doesn't really have anything to do with computers. People are often confused by negative numbers. Avoiding negatives is useful whether you use computers or not. Sure, the computer can handle negatives just as well as it handles positives. But people can't. I recall my ex-wife being totally baffled when we once overpaid a credit card and had a credit on our account. I forget the amount, say $20. She was going to send the credit card company $20 to pay it. I tried to explain to her that we didn't owe $20, the bank owed us $20. But she just couldn't comprehend that and that I was going to ruin our credit rating by not paying it.
As to having every number twice as a double check: Sure, computers are very reliable about arithmetic and it is VERY unlikely that the computer will make a mistake adding up a row of numbers.
Double entry bookkeeping doesn't JUST provide a backup. Say you buy a new machine for your factory with cash. We credit cash and debit capital equipment. How would you record that without double-entry bookkeeping? You'd still have to record the fact that you paid someone money, and you'd still have to record somewhere that you now have a new asset, this machine. Some double-entry bookkeeping entries may seem like unnecessary overhead just to accomodate the rule that debits and credits must be equal. But a lot of it just makes sense. You have to record that something went from X to Y.
Accountant have spent decades, maybe centuries, building and refining double entry bookkeeping. They have worked out ways to record all kinds of weird transactions. Like it's easy enough to say, "we paid $500 cash and got this product worth $500 in exchange". But what if you sold an item from inventory where the items in inventory were purchased at different times for different prices, and the buyer is not going to pay immediately but will pay in installments over some period of time, and part of the payment will be in cash and part will be a discount on future purchases that you make from them? How do you record that? An accountant can tell you.
Maybe you could develop another bookkeeping system that would not rely on double entry, but would still record everything you need to record. Take advantage of the computer's reliability at arithmetic to eliminate unnecessary duplication of data and data entry. But if you tried to invent such a system, you would then have to figure out how to record, not just the simple and obvious transations, but all the weird and complex cases.
And what would be the point? We already have a system that works. Why start over from scratch to make another one? You're certainly welcome to try to invent a new and better bookkeeping system. If you really come up with something good, maybe accountants would switch to it. But it would have to be enough better than the current system to be worth people investing the time to learn it and the time and effort to rework all their existing accounting software and procedures. Is it possible someone could invent such a system? Sure. Is it likely? I doubt it.
It would be like if someone said, "English has all these problems. I've invented a new and better language that we should use instead of English, with a whole different vocabulary and grammar." It wouldn't be enough to convince people that your new language was better. It would have to be enough better to be worth learning it and rewriting all existing documents.