2. A typical transaction has one input and two outputs. This implies a shortage of inputs available to cosign. How do you ensure that cosigners are available for each input and inputs are available for each cosigner?
It's only typical for consumers to create transactions that split coins. Merchants typically create transactions that merge coins. Sometimes the number of inputs will be less than the number of outputs, which will delay cosigners, and sometimes the number of inputs will be greater than the number of outputs, which will delay confirmations, but there will always be a natural average of 1:1.
I have to disagree with your assessment. The number of Bitcoin UTXOs has been climbing consistently, which means that the number of outputs has been consistently greater than the number of inputs.
A possible solution might be to require a transaction to cosign only one input for all of its outputs. However, that might create the reverse problem of not having enough transactions to cosign all the inputs (because there are more inputs than transactions). Perhaps the solution is to require a transaction to
signcosign a number of other inputs equal to the number of its inputs.