Can one measure the infeasibility of four color proofs? Terms like "impractical" and "unfeasible" are used to say the Robertson, Sanders, Seymour, and Thomas proof of the four color theorem needs computer assistance. Obviously no precise measure is possible, for many reasons.
But is there an informed rough estimate what a graph theorist would need to verify the 633 reducible configurations in that proof?  $10^4$ hours? $10^8$ years?
I am not asking if other proofs are known.  I want to know if graph theorists have an idea what scale of practicality we are talking about when we say the Robertson, Sanders, Seymour, and Thomas proof is impractical without machine assistance.
 A: As explained in Tony's answer, in order to answer this question you need to separately answer how long it would take to prove reducibility of the configurations (Theorem 2) and how long it would take to prove unavoidability of the configurations (Theorem 3).
There's an interesting alternate proof of the 4-color theorem due to John Steinberger, which differs from RSST in that the proof of reducibility only uses the easier notion of "D-reducibility" rather than the more elaborate "C-reducibility."  The cost is that the unavoidable set is much longer and the proof of unavoidability is also longer.  As Tony explained, unavoidability was the "easy" part, so it's possible that for a human Steinberger's proof would be easier to verify.  Even if it is not easier, he provides some additional detail of the estimate of "a few months" from RSST.
In discussing the proof of unavoidability, Steinberger discusses the files which serve as certificates of unavoidability.  That is, there's a file which tells the computer how to prove this particular case.  Of these files, in verbose human readable form, Steinberger writes:

While the resulting output may be readable at a normal pace it is also
quite large: over 3’000’000 lines for the Robertson et al. proof, over
13’000’000 lines for our proof. A mathematician checking these proofs
at the rate of one line per second and working 9 hours a day would
take over 3 months to read the Robertson et al. proof and over a year
to read ours.

This makes much more precise the "few months" estimate of RSST.
Unfortunately he does not give a human estimate for the reducibility portion.  Instead he says it takes a 2010 personal computer "around 10 hours."  If I understand things correctly, the problem here is that in order to check D-reducibility, you need to check something for every choice of 4-coloring on the boundary of your configuration.  For large configurations this is an enormous number of cases.  The computer time here large, which suggests that a human might prefer to do the RSST proof.
As discussed in the comments, a plausible estimate is that the Steinberger proof of reducibility would likely take somewhere between $10^4$ and $10^6$ hours (i.e. somewhere between a year and a lifetime).
A: To answer the question it is important to disentangle the proof as follows. 
Theorem 1. Every minimum counterexample to the 4CT is an internally 6-connected triangulation.
Theorem 2. If $T$ is a minimum counterexample to the 4CT, then no good configuration appears in $T$.
Theorem 3. For every internally 6-connected triangulation $T$, some good configuration appears in $T$.
See the actual paper for the definitions of these terms.  Theorem 1 does not require computer assistance, while Theorem 2 and Theorem 3 both do require computer assistance.  According to this version of the paper, Theorem 3 can in principle be checked by hand.  Indeed it is explicitly mentioned that 

It can be checked by hand in a few months, or a few minutes by computer (this was about 15 years ago though).  

I quote more on Theorem 3:

For each of these five cases we have a proof.  Unfortunately, they are very long (altogether about 13000 lines, and a large proportion of the lines take some thought to verify), and so cannot be included in a journal article.  

Theorem 2, on the other hand really requires a computer.  From the same paper, 

The proof of Theorem 2 takes about 3 hours on a Sun Sparc 20 workstation and the proof of Theorem 3 takes about 20 minutes. 

Thus, given that it took a computer 9 times longer to verify Theorem 2 than Theorem 3, and Theorem 3 apparently can be verified by hand in a few months (let us define few=3), then under some very dubious assumptions we have the ballpark answer of 
Ballpark Answer. 30 months. 
A: I'm not entirely sure of the intent of the question but, in general the feasibility of calculating an answer to a fixed sized problem is given by the non asymptotic computational complexity of the problem expressed as an algorithm and the processing power of the machine doing the calculation. Feasibility for a human calculator could be somewhat objectively derived in the same way by observing the processing power of the average human brain. I don't think there are established standards within the scientific community for about what threshold "feasibility" for a human calculator lies at. Normally one would assume "feasibility" would be qualified by some hard estimate of the time/effort required, as it is in this paper.
