It's not a tradeoff you are making, the fact is that your Arduino only has program space measured in the dozens KiB. If it doesn't fit, it doesn't fit.
But that's not the biggest problem. SQLite, like most programs, relies on having a C library like glibc available. This is pretty much the intermediary person to the operating system - you can ask it for memory, it will allocate memory for you, you can ask it to open a file, it will facilitate that. Most programs assume it's always present and so the dependency isn't properly abstracted. This is a problem when you don't have an operating system.
Notice also that you can't just go and implement or stub everything that glibc does. To do that, you would just end up having to add an operating system.
(This particular rabbit hole goes much deeper. A lot of programs sadly don't depend on a C library, they depend on glibc in particular. This causes massive problems for systems that run Linux yet can't accomodate glibc, like OpenWRT. They use an alternative C library that works fine 99% of the time, and for the remaining 1% it will cause programs to silently misbehave or crash because of an implicit dependency on whatever glibc does. I had this problem with the hwclock utility which started segfaulting when OpenWRT switched to musl libc)
But that's not the biggest problem. SQLite, like most programs, relies on having a C library like glibc available. This is pretty much the intermediary person to the operating system - you can ask it for memory, it will allocate memory for you, you can ask it to open a file, it will facilitate that. Most programs assume it's always present and so the dependency isn't properly abstracted. This is a problem when you don't have an operating system.
Notice also that you can't just go and implement or stub everything that glibc does. To do that, you would just end up having to add an operating system.
(This particular rabbit hole goes much deeper. A lot of programs sadly don't depend on a C library, they depend on glibc in particular. This causes massive problems for systems that run Linux yet can't accomodate glibc, like OpenWRT. They use an alternative C library that works fine 99% of the time, and for the remaining 1% it will cause programs to silently misbehave or crash because of an implicit dependency on whatever glibc does. I had this problem with the hwclock utility which started segfaulting when OpenWRT switched to musl libc)