Ditto Nate Eldredge in many ways, but let me add some other thoughts.
BTW there are not four types of account, but five. You're forgetting equity, also called capital.
Would it be possible to design an accounting system that does not have 5 types of accounts, maybe is simpler in other ways, and is internally consistent and logical? I'm sure it is. But what's the advantage?
As Nate points out, the existing system has been in use for hundreds of years. Lots of people know how it works and understand it.
I'd add: People have long since worked out how to deal with all the common situations and 99% of the odd cases you're likely to hit. If you invent your own system, you're starting from scratch. You'd have to come up with conventions to handle all sorts of situations. How do I record buying a consumable with cash? How do I record buying a capital asset with credit? How do I record paying off debts? How do I record depreciation? Etc etc. If you worked at it long and hard enough and you're a reasonably bright guy, maybe you could come up with solutions to all the problems. But why?
If you were approaching this saying, "I see these flaws in the way accounting is done today. I have an idea for a new, better way to do accounting", I'd say good luck, you have a lot of work ahead of you working out all the details to make a fully functioning system, and then persuading others to use it, but if you really do have a better idea, maybe you can revolutionize the world of accounting.
But, "The present system is too much trouble and I don't want to bother to learn it" ... I think that's a mistake. The work involved in inventing your own system is going to end up being way more than what it would take to learn the existing system.
As to, Aren't liabilities a lot like assets? Well, in a sense I suppose. A credit card is like a checking account in that you can use it to pay for things. But they're very different, too. From an accounting point of view, with a checking account you buy something and then the money is gone, so there's one transaction: reduce cash and increase office supplies or whatever. But with a credit card there has to be a second transaction, when you pay off the charge: So, step 1, increase debt and increase office supplies; step 2, decrease debt and decrease cash. Credit cards charge interest, well you don't pay interest to use your own cash. Etc.
One of the beauties of double-entry book-keeping is that every transaction involves a debit and a credit of equal amounts (or a set of debits and credits where the total of the debits equals the total of the credits). If you combine assets and liabilities into, whatever you call it, "balance accounts" say, then some transactions would involve a matching debit and credit while others would involve a positive debit and a matching negative debit and no credit. I'm sure you could make such a system work, but one of the neat built-in protections against error is lost.
There's a very logical distinction between things that you have or that others owe you, and things that you owe to others. It makes a lot of sense to want to list them separately and manage them separately. I think you'd pretty quickly find yourself saying, "well, we have two types of balance accounts, those that represent things we have and which normally have positive balances, which we list on chart A, and those that represent things we owe and which normally have negative balances, which we list on chart B". And before you know it you've just reinvented assets and liabilities.