Why do we need sulfuric acid in creating alkyl bromide and not in creating alkyl iodide from alcohol and hydrogen halide?
I suspect $\ce{HBr}$ is produced in situ from $\ce{KBr}$ and $\ce{H2SO4}$.

Same process isn't particularly suitable for $\ce{HI}$ generation as it reacts with $\ce{H2SO4}$:

$$\ce{2HI + H2SO4 -&gt; H2SO3 + H2O + I2}$$

I actually seriously doubt second reaction will take place at all. Hydroiodic acid can also act as a reducing agent, converting the resulting alkyl iodides to alkanes. Instead of $\ce{HI}$ is often being used $\ce{I2}$ with red phosphorous, or halide salts (Finkelstein reaction).



As @orthocresol noticed in the comment, the following two reactions are more preferable for alkyl iodides synthesis:

$$\ce{R - OH -&gt;[(C6H5O)3P+ CH3I-] R - I}$$

$$\ce{R - OH -&gt;[ (CH3 - S - CH = N+ (CH3)2) I- , THF] R - I}$$



Also, chapter 2.01.5.4 Alkyl Iodides from Alcohols, p. 16 in Comprehensive Organic Functional Group Transformations II (1) accumulates numerous ways of iodoalkanes synthesis:


  The adduct of triphenylphosphine with elemental iodine ($\ce{Ph3PI2}$)
  is a classic reagent used to convert alcohols cleanly and with
  inversion to iodides. Addition of imidazole is well known to promote
  this conversion with high yields. Furthermore, treatment of alcohols
  with triphenylphosphine and cyanogen iodide affords the corresponding
  iodides in good yields. The reagent $\ce{KI/BF3 * Et2O}$ in dioxane is
  highly selective and effective for the transformation of allylic and
  benzylic alcohols to iodides. 
  
  A mild and effective procedure for directly converting secondary,
  tertiary, and benzylic alcohols into the corresponding iodides
  involves treatment with iodine in refluxing petroleum ether. The
  reaction proceeds with inversion of configuration:
  
  
  
  Alkyl iodides can also be prepared in a single step from the
  corresponding alcohols upon treatment with the standard reagent
  $\ce{P-I2}$. A less well used reagent,
  1,2-bis-(diphenylphoshino)ethane, can be used to prepare iodides from
  primary alcohols in the presence of iodide. 
  
  Cerium(III) chloride, a Lewis acid imparting high regio- and
  chemoselectivity in various chemical transformations, can be used in
  combination with sodium iodide in refluxing acetonitrile to replace a
  hydroxy by an iodo group:
  
  
  
  This method cannot be applied to tertiary alcohols. In this case an
  alkene is derived by dehydration of the alcohol.
  
  Finally, a classical method for the transformation of alcohols to
  halides is the well-known two- step procedure via a sulfonate ester,
  commonly tosylate (p-toluenesulfonate) or mesylate (methanesulfonate).
  
  Treatment of the sulfonate esters with $\ce{NaI}$ or $\ce{LiI}$ gives
  iodides in good yields.


(1) Katritzky, A. R.; Ramsden, C.; Taylor, R. J. K. Carbon with One Heteroatom Attached by a Single Bond; Comprehensive Organic Functional Group Transformations II; Elsevier Science Ltd, 2004; Vol. 2. ISBN: 978-0-08-044253-2