If a window has keyboard events pending, SDL_PumpEvents or first call of SDL_PollEvent takes around 4-5 milliseconds which is too slow. For example, each frame of 60 fps game lasts only 1000/60 = 16.7 ms, and wasting 4 ms just for resolving keyboard events is huge performance issue. 

Here is minimal program to reproduce a problem. Tested on Debian 10. 

Mouse moving above the window causes only around 300 microseconds (0.3 ms) delay which is absolutely fine. But hitting even a single key increases delay to 4000+ microseconds. Holding a key probably "stacks" delay times up to 20-30 ms which is insane.

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#include <SDL2/SDL.h>
#include <time.h>

uint64_t get_time_us() {
    struct timespec tspec;
    clock_gettime(CLOCK_MONOTONIC_RAW, &tspec);
    uint64_t sec = tspec.tv_sec;
    uint64_t usec = tspec.tv_nsec / 1000;
    return sec*1000000L + usec;
}

int main (int argc, char ** args) {
    if( SDL_Init( SDL_INIT_EVERYTHING ) != 0 ) {
        return 1;
    }
    SDL_Window* window = SDL_CreateWindow("SDL2 Event Delay Test", SDL_WINDOWPOS_CENTERED, SDL_WINDOWPOS_CENTERED, 400, 300, SDL_WINDOW_SHOWN);
    if ( window == NULL ) {
        return 1;
    };
    int quit = 0;
    SDL_Event e;
    while ( !quit ) {
        uint64_t t[3];
        t[0] = get_time_us();
        SDL_PumpEvents(); // or it will be called on first SDL_PollEvent() and cause same delay
        t[1] = get_time_us();
        while( SDL_PollEvent( &e ) != 0 ) {
            if( e.type == SDL_QUIT ) {
                quit = 1;
            };
        };
        printf("SDL_PumpEvents() took %ld us (%ld ms)\n", t[1]-t[0], (t[1]-t[0])/1000 );
        SDL_Delay(100);
    };
    SDL_DestroyWindow(window);
    SDL_Quit();
    return 0;
};