Distance between a set of points and a polygon with sf in R

I have a dataframe of points on map and an area of interest described as a polygon of points. I want to calculate the distance between each of the points to the polygon, ideally using the sf package.

library("tidyverse")
library("sf")

# area of interest
area <- 
  "POLYGON ((121863.900623145 486546.136633659, 121830.369032584 486624.24942906, 121742.202408334 486680.476675484, 121626.493982203 486692.384434804, 121415.359596921 486693.816446951, 121116.219703244 486773.748535465, 120965.69439283 486674.642759986, 121168.798757601 486495.217550029, 121542.879304342 486414.780364836, 121870.487595417 486512.71203006, 121863.900623145 486546.136633659))"

# convert to sf and project on a projected coord system
area <- st_as_sfc(area, crs = 7415L)

# points with long/lat coords
pnts <- 
  data.frame(
    id = 1:3, 
    long = c(4.85558, 4.89904, 4.91073),
    lat = c(52.39707, 52.36612, 52.36255)
    )

# convert to sf with the same crs
pnts_sf <- st_as_sf(pnts, crs = 7415L, coords = c("long", "lat"))

# check if crs are equal
all.equal(st_crs(pnts_sf),st_crs(area))

I am wondering why the following approaches do not give me the correct answer.

1.Simply using the st_distance fun-doesn't work, wrong answer

st_distance(pnts_sf, area)

2.In a mutate call - all wrong answers

pnts_sf %>% 
  mutate(
    distance = st_distance(area, by_element = TRUE),
    distance2 = st_distance(area, by_element = FALSE),
    distance3 = st_distance(geometry, area, by_element = TRUE)
  )

However this approach seems to work and gives correct distances.

3.map over the long/lat - works correctly

pnts_geoms <- 
  map2(
    pnts$long, 
    pnts$lat, 
    ~ st_sfc(st_point(c(.x, .y)) , crs = 4326L) 
  ) %>% 
  map(st_transform, crs = 7415L)

map_dbl(pnts_geoms, st_distance, y = area)

I'm new to spatial data and I'm trying to learn the sf package so I'm wondering what is going wrong here. As far as i can tell, the first 2 approaches somehow end up considering the points "as a whole" (one of the points is inside the area polygon so i guess that's why one of the wrong answers is 0). The third approach is considering a point at a time which is my intention.
Any ideas how can i get the mutate call to work as well?

I'm on R 3.4.1 with

> packageVersion("dplyr")
[1] ‘0.7.3’
> packageVersion("sf")
[1] ‘0.5.5’