Finding centrelines from polygons in R sf

Question

Has anyone found a solution for turning polygons into centrelines using R? It has to be in R as I'm deploying it in parallel on a UNIX cluster. I've got as far as:

library(sf)    
centreline <- st_cast(polygon$geometry, "LINESTRING")

But this outputs the entire polygon boundary rather than the centreline.

Here are two solutions in ArcGIS and QGIS.

Creating Centrelines from Road Polygons/Casings using ArcGIS Desktop?

Finding centrelines from polygons in QGIS?

Sample data and code of what I've already tried:

Data

library(sf)
library(dplyr)

# inputs
linepath <- 'river.shp'
pointpath <- 'river_point.shp'
epsg <- 27700 

line <- st_read(dsn = linepath) %>% st_transform(epsg)

point <- st_read(dsn = pointpath) %>% st_transform(epsg)

# Buffer point 
bufferpoint <- st_buffer(point, dist = 1)  %>%
  st_transform(epsg) 

# Cut line with point
# A helper function that erases all of y from x:
st_erase = function(x, y) st_difference(x, st_union(st_combine(y))) 

splitline <- st_erase(line, bufferpoint) %>% 
  mutate(id = as.factor(row_number()))

buffered <- st_buffer(splitline, dist = 0.5) 

dissolved <- st_union(buffered) %>% as('Spatial') %>% st_as_sf()

singlepart <- st_cast(dissolved, 'POLYGON') %>%
  mutate(id = as.factor(row_number()))

centreline <- st_cast(singlepart$geometry, "LINESTRING")