Assuming primal simplex problem in form of
$$ \displaylines{ \begin{align} (P) & \\ \text{min} \ & c^Tx \\ \text{s.t.} \ & Ax = b \\ & -\infty \lt l \le x \le u \lt \infty \\ A \ \text{dimensions} : & \ m_p \times n_p, m_p \lt n_p \\ l, u \ \text{dimensions} : & \ 1 \times n_p \end{align} } $$
Where $m_p$ corresponds to number of constraints and $n_p$ corresponds to number of variables, with each $x$ having finite bounds, the dual of the same problem as given on pdf page 29 (rendered page 12) of The dual simplex method, techniques for a fast and stable implementation Elektronische Ressource appears to be
$$ \displaylines{ \begin{align} (D) & \\ \text{max} \ & b^Ty + l^Tv + u^Tw \\ \text{s.t.} \ & A^Ty + v + w = c \\ & v \ge 0 \\ & w \le 0 \\ \end{align} } $$
together with note "Then, we can treat the individual bounds (2.9c) like constraints and introduce dual variables".
Does that mean dualizing the problem would result in
$$ A^T+v+w \ \text{dimensions} : \ n_p \times (m_p + 2n_p) \\ $$
making the application of dual simplex computationally infeasible, as gains from dual algorithm version would be negated by increased problem size?
In other words, does that mean dual simplex can be considered a computational optimization only when $$ \text{length}(\{l: l > -\infty\}) + \text{length}(\{u : u < \infty\}) \lt n_p - m_p $$ and after that threshold it is more computationally efficient to solve the primal problem as is?