Why does fusing benzene rings not produce polycyclic alkynes?
The ideal bond angles for alkynes are $180^{\circ}$, which is necessary for optimal overlap of atomic orbitals combining to produce mutually perpendicular $\pi$-type molecular orbitals. Any significant deviation from this is normally inherently destabilizing. Rings, by the very nature of their geometry, often incur additional strain due to their conformational inflexibility and possible demands for non-ideal bond angles (relative to acyclic molecules, that is). Introducing $\pi$-bonds into rings can potentially compound this problem, since they force at least local planarity and shorter bond lengths. These factors all contribute to the immense instability of cyclic alkynes in general.

When you mention stable cycloalkynes, keep in mind that stability is a relative term in this context. While those with a sufficient number of carbons can be produced and isolated under specific experimental conditions, they are not thermodynamically stable relative to their open-chain equivalents, or to most of their various possible structural isomers. In some cases, they can, however, be made kinetically stable by the addition of flanking $\alpha$-substituents which inhibit reaction by their steric bulk1.

Syntheses of cycloalkynes below cyclooctyne are often elaborate, and frequently proceed through extremely reactive intermediates that decompose by specific reaction pathways so as to carefully avoid other products. Benzene (and the various polycyclic aromatic hydrocarbons, for that matter), on the other hand, is an extremely stable molecule which participates in quite a limited collection of reactions. Whatever particular reaction you're suggesting would almost certainly be hugely uphill in energy (i.e., yields a significantly less stable product), and hence very thermodynamically disfavored; it would also certainly have immense kinetic barriers as well (since any such reaction pathway implies at least temporary loss of aromaticity in the transition state[s] and intermediate[s]).

Relevant reading might include Dehydrobenzene and Cycloalkynes by Reinhard W. Hoffmann. There is extensive discussion of the reactivity of cycloalkynes, and numerous examples of spontaneous dimerizations, isomerizations, etc. Evidently, isomerizations to cycloallenes and cyclobutadiene dimers are common, which is a profound testament to the instability of cycloalkynes.

1. For example, 3,3,7,7-tetramethylcycloheptyne, a good description of which (and synthetic scheme for) is given in Strained Hydrocarbons by Dodziuk.