It’s not about “giving secret information to a foundry”. It’s entirely the field programmable (FP) feature. It’s also not really programmable in the sense that you would be sending in new instructions in realtime. Reconfigurable is a better word. So giving everyone an FPGA in their laptop isn’t really going help anyone in except some enthusiast who wants to try out some different algorithms.
Many high-frequency trading companies use FPGAs over ASICs for similar reasons. FPGAs are more expensive but allow them to have full control over the algorithms implemented and doesn't require giving secret information to a foundry.
In other words, eliminate the impedance mismatch between responsibility and control for developing a secure system.
It'll be cheaper to implement cryptography on an ASIC. But the author of this paper wants to control every single aspect of the encryption/decryption process. Said developer can confidently say the system is secure. You can't say you've delivered a secure system if you're getting your ASICs from another company that doesn't provide implementation details because it'd (justifiably) give others a competitive advantage.
Question I'd have is whether the cost difference between ASICs/FPGAs is worth it for the majority of applications. $1 or $10 on every CPU might mean a world in which every laptop has an FPGA, but $100? What about for server-side applications? Would a hyperscaler spend $1000 extra on every rack if it allowed guaranteed constant-time encryption?