plotly::subplot() not producing the interactive equivalent of gridExtra::grid.arrange()

Question

Given:

    library(ggplot2)
    library(gridExtra)
    library(plotly)
    library(colorRamps)
    
    d <- data.frame(x=sample(1:10)/10, y=sample(1:10)/10, z=sample(1:10)/10, c=sample(LETTERS[1:5],size=10,replace=TRUE))
    g1 <- ggplot(d) +
      geom_point(aes(x=x, y=y, fill = z),
                 pch=21,size=4) +
      facet_wrap(~c,labeller = label_both) +
      scale_fill_gradientn(colors = matlab.like2(16),limits=c(0, 100)) +
      xlim(c(0,1)) + ylim(c(0,1)) +
      coord_fixed(ratio = 1) +
      theme(legend.position=c(0.85,0.2), legend.background=element_blank()) +
      labs(fill = "%")
    
    g2<- g1+ggtitle("Plot 2")
    g3<- g1+gtitle("Plot 3")
    g4<- g1+ggtitle("Plot 4")
    g1<- g1+ggtitle("Plot 1")
    p = list(g1,g2,g3,g4) %>% map(~.x + labs(x=NULL, y=NULL))
    yleft= "X"
    xbottom= "Y"
    grid.arrange(grobs=p,bottom = xbottom, left = yleft,nrow=2)

I want to get the same plot but with interactive browsing of the values. I try:

pg1 <- ggplotly(g1)
pg2 <- ggplotly(g2)
pg3 <- ggplotly(g3)
pg4 <- ggplotly(g4)

Individual plots are ok:

pg1

But

subplot(list(pg1, pg2,pg3,pg4), nrows=2, 
        shareX=FALSE, shareY=FALSE,titleX=TRUE,titleY=TRUE)

or

subplot(list(pg1, pg2,pg3,pg4), nrows=2, 
        shareX=FALSE, shareY=FALSE,titleX=FALSE,titleY=FALSE)

result into:

Which is almost good but displays only 1 title (and in the wrong place) and no axes titles.

I try

subplot(list(pg1, pg2,pg3,pg4), nrows=2, 
        shareX=TRUE, shareY=TRUE,titleX=FALSE,titleY=FALSE)

and

subplot(list(pg1, pg2,pg3,pg4), nrows=2, 
        shareX=TRUE, shareY=TRUE,titleX=TRUE,titleY=TRUE)

and the result is even worse

Is there a correct way to get the interactive graphic I am looking for?