To use OBS, you need better hardware and network infrastructure.
Your CPU/GPU combination is too weak to be doing 1080p, let alone 720p. Also, streaming via wireless is not recommended. You should use a fixed Ethernet connection instead.
You need a better computer and to not be using Wifi.
I shall have to correct you on this misinformation you seem to be offering.
The computer has zero problems encoding as it uses the Intel QuickSync video HARDWARE encoder. NO strain on system resources happens at all. OBS will quite happily stream for hours, but then randomly freeze for apparently no reason. The statistics show a healthy stream with no underruns or encoding lag, ever. The numbers speak from themselves. The hardware is totally capable of rendering a canvas with the integrated Intel graphics and then encoding the resultant video with the Intel QuickSync HARDWARE video encoder.
The hardware here is not the issue as I have monitored the system resources during streaming with these exact settings, regardless of being on wifi or wired ethernet. System resource monitors show that CPU, memory and network usage are all minimal and not bottlenecking at all during a 1080p 30fps 1.2mbps stream.
I use this with 4 different networks that are professionally configured. The wired networks are multiple gigabit SFP+ linked and administered by qualified personnel as are the wireless networks I use which are wireless AC MIMO routers which have no interference or bandwidth problems. All channels are steered away from competing routers and the radio spectrum here is relatively uncluttered. I can easily attain 100mbps+ wireless speeds and very low latency in this wireless environment. The hardware used includes Netgear Nighthwak and better routers so this shouldn't be an problem. I have no trouble streaming any 4K content, downsampling and playing the video on this hardware. I also have no issue streaming live 1080p video from this computer using any other software, either from 1080p webcams or from virtual cameras that are transcoding the video in realtime.
I have streamed video from lesser processors and lesser memory with OBS no problems, so the hardware is not at fault here or too weak to run any encoding job.
The overlays are minimal, just showing one browser source from OctoPrint on a Raspberry Pi and there are no video filters applied and as the webcam is running at native resolution there is no video scaling either, so the system is free to encode a relatively light canvas at 1080p 30 fps at a relatively low 1.2MBPS. There's also no audio processing as the stream is silent.
A core i5 2.6GHz processor (with HARDWARE Quicksync H264 video encoding!), Windows 10 64 bit and 8GB of RAM and Samsung EVO 860 SSD is more than adequate to encode video and stream it over a gigabit ethernet connection, especially when there is a simple canvas in OBS, streaming just one native resolution video source, one 2D browser source and two GDI text overlays, so please don't try to tell me otherwise, I know my tech.