Why doesn't Windows 11 support i7 7500? Is there a way to install it?

actually you can do the bypass route and not worry about anything going wrong, its actually really simple using the Rufus USB boot-disk utility. here is how you do that: first backup all your important personal data so that you don't lose anything that you are set on needing to keep. no-brainer right? then you download the latest Microsoft Windows 11 .ISO file which you can obtain easily strait from Microsoft Download Center.  you will need a USB flash drive, i recommend using one with a minimum capacity of 16GB; download the Rufus app (its free) and install. open the app after its installed and at the top of the window that opens when you open Rufus you will see the label of the flash drive you chose to make a Windows 11 Boot Disk with listed as the destination disk and a box to the right of it that you click to select the .ISO File you are wanting to make into the boot disk.  in this case obviously the Windows 11 .ISO file that you download for this task, in the following box marked Image Option, you can leave that set to Standard Windows Installation, then in the Partition Scheme box you set it to GPT, the next box you can leave it set to the UEFI (non CSM) setting that will already be shown, the only other setting in that window you will need to pay attention to is making sure the file system setting is set to NTFS in the drop box , and under the STATUS line it should read as 'READY', if so, click the start button.  right after you click the start button in the Rufus app  a window will appear with the label 'windows user experience' asking about customizing windows installation, you have to check the top box that sets it to bypass the 4GB+ Ram, Secure Boot and TPM 2.0 requirements that the windows 11 installer would normally check during the beginning of installing windows 11 on your machine, personally i check every box in that window, type the username for the local account where it has a box to do so on the third option in the list and hit OK, the Rufus app goes to work making your flash drive into a bootable windows 11 disk which you will leave in the USB port after Rufus completes its process and you reboot your computer, after that the windows 11 OS installer will be as it always looked, read everything carefully so that you choose the options that are needed for your computer to have the options most suitable for your needs as you normally would when installing windows on a computer, give it one last go over to ensure everything is how you would like it and hit install, that's it.  I've installed windows 11 pro successfully on my Lenovo ThinkPad T430 which only has the TPM 1.0 and a 3rd gen core i5 dual core CPU and 8GB of DDR3 ram, and a 1TB SATA II SSD drive without any issues and surprisingly for a lappy from around 2013 it runs windows 11 pretty smoothly, I also successfully installed it on a Desktop PC running a 3rd gen core i5-3570k quad core CPU, 32GB DDR3, and a PNY 1TB SSD, again without any issues and it to runs windows 11 really Smoothly without any noticeable lagging that i can see, both machines get and install updates as the normally would when they are released without problems.  Hope this step by step guide helps you as much as it has me, it definitely helps keep perfectly capable machines from going to waste un-neededly, along with saves you any un-warranted upgrade costs too, ENJOY!