If I buy a computer for $2000 it goes on my asset sheet at $2000 and depreciates over time according to GAAP rules. Shouldn't my lease contract on a $1000/month

If I buy a computer for $2000 it goes on my asset sheet at $2000 and depreciates over time according to GAAP rules. Shouldn't my lease contract on a $1000/month 5 year contract be a $60,000 asset and a $60,000 liability with the asset depreciating at $1,000/month? In most of accounting we get double entry bookkeeping to work by assuming the cost paid for an asset is the value of the asset. I think in many cases reporting it this way would be more accurate (Although depreciation expenses would be a giant loophole that needs fixing).