They had doors and window shutters (and even some glazed windows)! But the fancy elongated vistas that often made elite houses into spectacles required that these doors and windows be open in order to be effective, and doors aren't often archaeologically preserved because of their materials, so they often just get left out of reconstructions. For the purposes of making something like a movie, the effect of the open vista and showing the size and extent of the property is probably more important than accuracy.

There are a few doors left over from the ancient world. The giant bronze doors of the Roman Curia were re-installed at the Church of St. John Lateran in Rome and remain there to this day. Most monumental bronze items, like any very fancy doors for very important buildings other than the senate house, ended up melted and repurposed at some point during antiquity. Most doors were made of less permanent materials that decay in most conditions, like wood. Archaeologists find a lot more locks and keys and bolts than they do actual doors. They find even more thresholds, with things like hinge plates and grooves that indicate where a door once hung or a sliding panel was tracked. There are, luckily, exceptions from the usual suspect sites like Pompeii and Herculaneum, where extreme conditions led to better preservation and we have things like the carbonized wood sliding doors at Herculaneum's House of the Wooden Partition (III.11) and the casts taken of imposing double-leaf front doors at several Pompeiian houses. These examples, where we can link a specific type of door to the kind of permanent markings it might leave in the surrounding architecture, allow archaeologists to speculate about what kinds of enclosure systems existed at sites where preservation is less complete.

The other thing that I think you might be thinking about, describing a wall around households that are open on the inside, are peristyles and courtyards within the property walls. These were very common in both Greek and Roman houses, and you wouldn't necessarily have doors installed on every room in an ancient house, including on some that might open from these spaces, which were interior to the property line even if they might open onto the outdoors.

I hate to self-cite, but I answered a question about privacy in the Roman world last week here that went into the ways that more elite houses in the city were kind of public spaces, with doors open to the public at least at certain times of the day. But this doesn't mean that they didn't have the capacity to be shut up at night, for example, and thievery was rampant and one reason why so few urban houses have ground floor windows. In the countryside, there is some evidence that properties may have been originally at least partly open to the public. I'm thinking specifically of the propylon at the Villa of Poppaea at Oplontis, which has four very tall columns/pilasters, with hinge plates that seem to have been inserted later than the mosaic of the threshold since they cut through the pattern. While there might have been an earlier enclosure system, it is also possible that the room behind the columns was originally open on the front. It's also worth mentioning that in this case, the room doesn't actually lead anywhere within the villa; all of the spaces it connects to that go further inside did have the ability to be closed off. So it could achieve the impressive effect of a large open front without actually assuming much risk of a home invasion.

Pretty much everything I know about ancient doors I learned from M. Taylor Lauritsen, two of whose articles are cited here:

Lauritsen, M. T. (2012). The Form and Function of Boundaries in the Campanian House. In Anguissola, A. (Ed.), Privata Luxuria: Towards an Archaeology of Intimacy, (pp. 95–114). Munich: Herbert Utz Verlag.

Lauritsen, M. RT. (2015). Ter Limen Tetigi: Exploring the Role of Thresholds in the Houses of Pompeii and Beyond. In A.A. Di Castro, C.A. Hope & B.E. Parr (Eds.), Housing and Habitat in the Ancient Mediterranean. Cultural and Environmental Responses (Babesch Supplement 26, pp. 299–312).

If you want to learn more about Oplontis and its thresholds in particular:

Lea Cline's chapter in the Oplontis Project excavation's publication volume 2, which is an ACLS open access ebook and available here.