Nomenclature of Halogen substituted Alcohol and longest chain
Your rationale is correct.

The proposed name “4-chloro-3-ethyl-2-(1-methylethyl)-butan-1-ol” is unambiguous and describes the correct compound; however, it is not in accordance with IUPAC nomenclature.

The important simplified criteria for the choice of a principal chain in such compounds are:


greater number of suffixes (here: “-ol”)
longest chain
lower locants for suffixes
greater number of prefixes (e.g. “chloro-”)
lower locants for prefixes
lower locants for substituents cited first as a prefix in the name


The corresponding wording of the nomenclature rules (taken from Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book)) reads as follows:


  P-44.1 SENIORITY ORDER FOR PARENT STRUCTURES
  
  When there is a choice, the senior parent structure is chosen by applying the following criteria, in order, until a decision is reached. These criteria must always be applied before those applicable to rings and ring systems (see P-44.2) and to chains (see P-44.3). Then criteria applicable to both chains and rings or ring systems given in P-44.4 are considered.
  
  P-44.1.1 The senior parent structure has the maximum number of substituents corresponding to the principal characteristic group (suffix) or senior parent hydride in accord with the seniority of classes (P-41) and the seniority of suffixes (P-43).
  
  (…)
  
  P-44.3.2 The principal chain has the greater number of skeletal atoms [criterion (b) in P-44.3].
  
  (…)
  
  P-44.4.1 If the criteria of P-44.1 through P-44.3, where applicable, do not effect a choice of a senior parent structure, the following criteria are applied successively until there are no alternatives remaining. These criteria are illustrated in P-44.4.1.1 through P-44.4.1.12.
  
  The senior ring, ring system, or principal chain:
  
  (…)
  
  (h) has the lower locant for an attached group expressed as a suffix (P-44.4.1.8);
  
  (…)
  
  P-45.2.1 The preferred IUPAC name is based on the senior parent structure that has the maximum number of substituents cited as prefixes (other than ‘hydro/dehydro’) to the parent structure.
  
  P-45.2.2 The preferred IUPAC name is based on the senior parent structure that has the lower locant or set of locants for substituents cited as prefixes (other than ‘hydro/dehydro’) to the parent structure.
  
  P-45.2.3 The preferred IUPAC name is based on the senior parent structure that has the lower locant or set of locants for substituents cited as prefixes to the parent structure (other than ‘hydro/dehydro’ prefixes) in their order of citation in the name.


Therefore, the preferred IUPAC name for the compound that is given in the question is 3-(chloromethyl)-2-(propan-2-yl)pentan-1-ol.



The position of the chloro group or other substituent groups that are cited as prefixes is not relevant for the choice of a principal chain in this case. Only if there is still a choice, such substituent groups are taken into account according to P-45.2.