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

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 this a bug or am I doing something wrong? Is there an alternative way to get the interactive version of the grid?

Start with the reproduced ggplotly() and subplot() calls in the issue, comparing their output with grid.arrange(). Trace how subplot() handles multiple plot titles, shared axes, and axis titles. Done means the four converted plots retain the expected titles and axes in a two-row interactive arrangement, or the behavior is documented as a limitation.