The problem is that the cost [ of validating a transaction ] grows like N^2 for N inputs.
By the way, there is no excuse for the cost to be quadratic. That is one of the many crocks in the BitcoinCore implementation, that will take more crocks to work around. Like the Segregated Witnesses proposal, malleability and its partial patches, blockchain voting to increase the limit, etc..
There you have another possible failure mode for Bitcoin:
runaway code crockification (RCC). As the code gets more complicated and ugly, fewer competent people will be willing to work on it. Their place will be taken by incompetent pople, who will add even more crocks -- and so on until the code will fail and there will be no one capable of fixing it in time.
Just a possibility; but after seeing the malleability problems, the Fork of July fiasco, the "fee merket" plans and the RBF hack, the Seg Wit proposal -- I fear that the RCC may be already underway...