Download managers tend to use multiple streams which copyurl does not do. You can do something like this and up the streams if you want.
Here is how it works to figure out number of streams:
https://rclone.org/docs/#multi-thread-cutoff-size
felix@gemini:~$ rclone copy --http-url http://ipv4.download.thinkbroadband.com :http:1GB.zip /home/felix -vv --multi-thread-streams 8 --multi-thread-cutoff 128M
2021/03/13 09:06:21 DEBUG : rclone: Version "v1.54.1" starting with parameters ["rclone" "copy" "--http-url" "http://ipv4.download.thinkbroadband.com" ":http:1GB.zip" "/home/felix" "-vv" "--multi-thread-streams" "8" "--multi-thread-cutoff" "128M"]
2021/03/13 09:06:21 DEBUG : Creating backend with remote ":http:1GB.zip"
2021/03/13 09:06:21 DEBUG : Using config file from "/opt/rclone/rclone.conf"
2021/03/13 09:06:21 DEBUG : Creating backend with remote "/home/felix"
2021/03/13 09:06:22 DEBUG : 1GB.zip: Need to transfer - File not found at Destination
2021/03/13 09:06:22 DEBUG : 1GB.zip: Starting multi-thread copy with 8 parts of size 128M
2021/03/13 09:06:22 DEBUG : 1GB.zip: multi-thread copy: stream 8/8 (939524096-1073741824) size 128M starting
2021/03/13 09:06:22 DEBUG : 1GB.zip: multi-thread copy: stream 4/8 (402653184-536870912) size 128M starting
2021/03/13 09:06:22 DEBUG : 1GB.zip: multi-thread copy: stream 6/8 (671088640-805306368) size 128M starting
2021/03/13 09:06:22 DEBUG : 1GB.zip: multi-thread copy: stream 7/8 (805306368-939524096) size 128M starting
2021/03/13 09:06:22 DEBUG : 1GB.zip: multi-thread copy: stream 3/8 (268435456-402653184) size 128M starting
2021/03/13 09:06:22 DEBUG : 1GB.zip: multi-thread copy: stream 5/8 (536870912-671088640) size 128M starting
2021/03/13 09:06:22 DEBUG : 1GB.zip: multi-thread copy: stream 1/8 (0-134217728) size 128M starting
2021/03/13 09:06:22 DEBUG : 1GB.zip: multi-thread copy: stream 2/8 (134217728-268435456) size 128M starting
2021/03/13 09:06:34 DEBUG : 1GB.zip: multi-thread copy: stream 1/8 (0-134217728) size 128M finished
2021/03/13 09:06:37 DEBUG : 1GB.zip: multi-thread copy: stream 5/8 (536870912-671088640) size 128M finished
2021/03/13 09:06:38 DEBUG : 1GB.zip: multi-thread copy: stream 4/8 (402653184-536870912) size 128M finished
2021/03/13 09:06:40 DEBUG : 1GB.zip: multi-thread copy: stream 8/8 (939524096-1073741824) size 128M finished
2021/03/13 09:06:43 DEBUG : 1GB.zip: multi-thread copy: stream 2/8 (134217728-268435456) size 128M finished
2021/03/13 09:06:45 DEBUG : 1GB.zip: multi-thread copy: stream 7/8 (805306368-939524096) size 128M finished
2021/03/13 09:06:50 DEBUG : 1GB.zip: multi-thread copy: stream 3/8 (268435456-402653184) size 128M finished
2021/03/13 09:06:53 DEBUG : 1GB.zip: multi-thread copy: stream 6/8 (671088640-805306368) size 128M finished
2021/03/13 09:06:53 DEBUG : 1GB.zip: Finished multi-thread copy with 8 parts of size 128M
2021/03/13 09:06:53 INFO : 1GB.zip: Multi-thread Copied (new)
2021/03/13 09:06:53 INFO :
Transferred: 1G / 1 GBytes, 100%, 32.103 MBytes/s, ETA 0s
Transferred: 1 / 1, 100%
Elapsed time: 32.2s
2021/03/13 09:06:53 DEBUG : 18 go routines active
as an example.