The filter isn’t for external foreign substances, it’s for internal debris that is inevitable from normal wear. Some parts of an automatic transmission (valves in the valve body) are VERY susceptible to even tiny particles. It’s common practice to have one or more magnets in the bottom of the pan to collect dust-sized “iron filings,” as a supplement to the filter.
In most* automatics, access to the filter is by removing the transmission’s bottom pan. Obviously, this drains the fluid. American-design pans almost never have a drain plug, but even if they did, the pan still has to come off to replace the filter. This is the essence of a traditional service - remove the pan, drain the fluid, replace the filter, replace the pan with a new pan gasket, replace the fluid with new.
Flushing is accomplished by disconnecting a joint in a transmission cooler line, pumping fresh fluid into one part of the line while collecting old fluid from the other. When only fresh fluid comes out of the exit line, virtually all of the fluid has been changed. Since the pan isn’t removed to do this, the filter is not accessed.
To change all of the fluid AND change the filter, both processes must be done. This is superior to doing just one or the other, but obviously costs more than either process alone. Many (too many) shops push the flush, touting its benefit of replacing all the fluid, while overlooking filter replacement. This is probably because they have an expensive flushing machine whose cost they want to justify, and flushing is quicker and easier than a traditional service. There is more money to be made by flushing, particularly once the machine has been paid off. There’s nothing wrong with flushing, and it does have a real benefit, but never changing the filter can be a problem. And of course if they try to sell both services together, they appear too expensive compared to selling just one service like everybody else does.
Hence my recommendation to alternate the types of transmission servicing. For decades, only traditional services were done, so not changing ALL the fluid isn’t awful. And filters can last many tens of thousands of miles, so not ALWAYS replacing the filter isn’t awful. But the maximum benefit comes from covering both bases. I suggest the first service be a traditional one, because the break-in of a new transmission produces more debris than normal operation after break-in.
A traditional tranny service is a lot messier than an engine oil change, especially if there’s no pan drain plug. Draining is accomplished by removing most of the pan bolts and letting the pan drop on one side. This sends a big splash of fluid over a wide area. Special oversized tranny drain pans are made for this purpose. After the fluid is drained and the pan completely removed, fluid will drip from anywhere in the pan coverage area. Pans are attached with hex-head bolts, requiring normal socket wrenches. Filters are attached with hex-head bolts, Phillips-head screws, or just pressed in.
Care must be taken to note any gasket or seal associated with the filter - leave the old one or install the new one, but don’t put a new one in on top of the old one. Clean all the debris off the magnet(s), and wipe the inside of the pan clean. If the new pan gasket is cork, tighten it in several stages allowing 5+ minutes “rest” between each stage for the cork to settle, and DON’T OVERTIGHTEN. Refilling is done through the tranny dipstick tube, and requires a special narrow-necked transmission funnel. Often it’s impossible to read the dipstick right after adding fluid - you get a false high reading from fluid working its way down. Time must be allowed for the fluid to settle from the dipstick tube.
*There are some exceptions. A few designs have an external spin-on filter, like an engine oil filter. In these cases flush plus filter replacement makes sense, and the pan doesn’t have to be removed. And some (only Honda and Acura to my knowledge) have no pan - the filter can only be removed by disassembling the tranny, and thus is not changed as maintenance.