Anyone here know woodworking?

I don't do eastern carpentry. Although there are times a pull saw is nice, its not a match for the angllo-eurpean techniques discussed above.

Yes - its likely the saws that came with the cheaper mitre boxes may not be sharp or have other tweaks needed. Could be technique too but not enough info to guess at that.

The 11" Tennon saw here would be an OK deal.
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I' d prefer no broken teeth at that price, but it is sharpened by a pro.

For new at reasonablish prices, see what Veritas and lee Valley have. But they can be on the pricey side but are known for quality.
There are several US importers of Pax and Lynx saws from Thomas Flynn (UK) and even shipped across the Atlantic prices aren't too bad.

Tonight I can look for more links to folks who sell used saws sharpened and ready to go.

The larger saws, like 5to 6 tpi rip saw are not difficult to sharpen. The small toothed saws are more difficult IMO.