Why would a polar protic solvent favor the addition of HBr to an alkene?
why a protic solvent?

Protic solvents tend to have higher dielectric constants than typical, unreactive, non-protic solvents.  Look at the following table.
\begin{array}{|c|c|c|}\hline
\text{Solvent} &amp; \text{Dielectric constant}    \\ \hline
\text{methanol} &amp; 32.6    \\ \hline
\text{ethanol} &amp; 24.6   \\ \hline
\text{methylene chloride} &amp; 9.08 \\ \hline
\text{chlorobenzene} &amp; 5.69\\ \hline
\text{chloroform} &amp; 4.81    \\ \hline
\text{diethyl ether} &amp; 4.27    \\ \hline
\end{array}
The higher dielectric constant stabilizes ions which means that 1) $\ce{HBr}$ will tend to be more dissociated and 2) (as Dissenter noted) the resultant carbocation intermediate will be more stabilized thereby lowering the energy of the transition state leading to it.