The cost of a building and filming a model shuttle, and more importantly building the full-size mockup and interior set that your actors need to use, is a significant outlay. This is why neither TOS nor TNG did it until later in their run. It's much easier now with CGI, as Enterprise proved and Orville still does, but even in the late 80s and early 90s convincingly mocking up shuttles wasn't straightforward.
Further to this – there's a few episodes early in TOS where shuttles are not even mentioned as a possibility and it seems like the transporter is the only way to get to or from the ship, most notably "The Enemy Within". Shuttles weren't mentioned at all until "The Galileo Seven", the production of which had to be delayed for two months because the Desilu studio executives wouldn't authorise the cost of the shuttle prop – in fact they held off until they secured a model kit deal with AMT, which offset some of the costs (and also meant they could sell models of the shuttle).
TNG didn't show a shuttle for the first time until "Coming of Age", and the
Type 7 shuttle as seen on screen was already a cut-down version of the
much larger original TNG shuttle concept. In the end event the shuttle cockpit for season one was only a partial build – hence the awkward camera angles – and the Type 7 was never realised as a full-size prop, with partial mock-up exteriors being faked a few times. The whole reason TNG started to use that little boxy
Type 15 shuttlepod so often from season two on was because it was
cheap – and well it might be, it looks like a flat-pack from Ikea ("Sjüttl"?). The
Type 6 introduced in the fifth season came about because the prop and set were modified from the
one built for Star Trek V: The Final Frontier.
Voyager's production team wanted a
more streamlined shuttle from the off but weren't able to budget for it until the second season; the
Type 8 used in
Voyager's first season came about precisely because the interior of the Type 6 could be used almost completely unmodified, since it was basically a Type 6 with
Voyager-ified nacelles.
Finally – just to show how difficult shuttles can be on a show's budget, let's look at
seaQuest DSV. What, really? Well why not, it was basically a TNG knockoff on a submarine. And while they didn't have shuttles in the space sense they did have launches, which were underwater shuttles that could also crawl onto land to enable them to get onto beaches and other places that didn't have a convenient docking port. In some first season episodes they tried to fake having a physical launch prop...
by sticking a big cardboard cutout of one in the background while people milled around in the foreground and some hapless director hoped depth of field blurriness would make it look convincing. This never looked anything other than embarrassingly fake – and
seaQuest DSV had a bigger budget than TNG, at least initially ($1.5m vs $1.25m per episode), plus they didn't have to worry about building physical models for all their effects shots since they were 100% CGI.
Edited to fix a spelling issue.