Your "master key" has value only insofar as its public part can be used to verify that which was signed with it; and this includes other people. For instance, your "master key" is your ultimate resource to revoke sub-keys. So if you mind about interoperability, then you cannot make the master key as big as you would wish, even if your GnuPG binary has been compiled with appropriate support.
Of course, other people could use your sub-keys only, but what would be the point of the master key then ? If people have to trust your sub-keys by out-of-band means, without getting up to your master key, then the sub-keys are really master keys in their own right. If you want sub-keys to be really "sub", and the master key to be the "master", then you have to use a master key that other people can use (i.e. verify signatures made with the master private key).
As the standard says:
* OpenPGP does not put limits on the size of public keys. However,
larger keys are not necessarily better keys. Larger keys take
more computation time to use, and this can quickly become
impractical. Different OpenPGP implementations may also use
different upper bounds for public key sizes, and so care should
be taken when choosing sizes to maintain interoperability. As of
2007 most implementations have an upper bound of 4096 bits.
First sentence is technically wrong, because the format for big integers used in OpenPGP (the "MPI") works "only" up to 524280 bits (which is still quite large). The important point is that back in 2007, using a key of more than 4096 bits incurred the risk of interoperability issues. Given the pace at which people, as a whole, upgrade their software, it would be inordinately optimistic to assume that bigger keys can be used everywhere in 2014.
As for performance, it rarely matters for emails, because emails happen at human pace, so using a "slow" algorithm is not much of an issue as long as it still happens in less than one second. Usual RSA implementations are cubic in key size, meaning that signing with a 4096-bit key will be 64 times slower than signing with a 1024-bit key; therefore you do not want to use really huge keys. However, interoperability issues will bite you much sooner than performance issues.
Right now, in April 2014, no properly generated 1024-bit RSA key has ever been broken publicly. Academics have long worked on the subject, and have come to the conclusion that breaking a 1024-bit key is feasible with existing technology, but entails building a dedicated machine with a very specific architecture, for a cost of several dozens of millions of dollars (even if the work force is "free", i.e. PhD students). In that sense, 1024-bit RSA is in a situation reminiscent to what 56-bit DES was in the early 1980s. Larger keys, e.g. 1536 bits, are way beyond current Earth-based technology. Even with a very optimistic prediction of technological advances, 2048-bit RSA keys ought to be fine for at least 30 years, probably more.
4096-bit keys are overkill, and can be "rationally" justified only as a way to quiet your own paranoia. 8192-bit keys are just plain wrong.
Now, of course, one may imagine that there could be a mathematical advance, in the form of a half-crazed mathematician from some remote location you've never heard of, finding a nifty and efficient way to solve integer factorization. This is highly speculative. Believing that a bigger key would still thwart that hypothetical breaking method is piling speculation on speculation: hardly a sane way to evaluate risks. In fact, physicians have already come up with an efficient method to break RSA, called a quantum computer. Fortunately (or not ?), building a working QC of non-ridiculous size appears quite hard. The important point here, though, is that a 8192-bit RSA key is not really stronger than a 2048-bit RSA key when the attacker has a QC.
Remember that security is an all-encompassing field. That you use OpenPGP with big keys does not mean that attackers are compelled to attack you only through breaking your key. Breaking through your door and planting a hidden video camera in your apartment are effective and way cheaper ways to spy on you. If your secrets are really interesting enough to warrant attention from bad guys, then they will use physical eavesdropping methods that are known to work, have been used for centuries, and have a moderate cost; bigger RSA keys won't change anything to it.
(On the other hand, using stupendously huge RSA keys may send the signal that you are an unrealistic crackpot, and being classified as "harmless fool" is a good way to evade deep scrutiny. This could work.)