Both the TOH and the device page says that the last version to support the TL-WR741ND v4 is 18.06.7. The download page for 19.07.1 does list the device, but only the initramfs-kernel image is available.
I try the Image Builder 19.07.1 and it still lists that device as supported, and I can build images for it. By default, the output
factory image is 3.8MiB, while the
sysupgrade image is 3.2MiB, meaning they will fit.
Why are these images not available on the download page?
Because of https://openwrt.org/supported_devices/432_warning
While support for these devices hasn't been actively removed (on the contrary), the buildbots haven't succeded to build 19.07.x images for most affected devices, as the default package set simply no longer fits. Using imagebuilder you can reduce this a bit more (e.g. luci, opkg and maybe ppp are the easiest ommissions), but looking forward that has its limits as well so you should schedule a hardware replacement.
OpenWrt won't publish any further release images for these devices (snapshots, by the virtue of omitting luci, might be available a little longer, but in the medium term the buildbots will skip the tiny targets alltogether).
I am fine without LuCI. But is it safe to use the images from the Image Builder on these devices? I mean, is there any chance that the Image Builder [by default:
make image PROFILE=xxx] omits some important packages such as networking or SSH, and I end up with a non-accessible device?
The imagebuilder will do what you ask it to do, including 'unhealthy' configurations. You are at the helm, use your powers wisely and within the knowledge that your warranty is void.